UMIT Seminar Series

Past Events and Seminars

2025

2025 Friday May 23rd - 14.05

Title: How do neural networks react to symmetries in the data?

Speaker: Axel Flinth, Mathematics, UmU

Abstract: There is an ongoing debate on how symmetries in data should be handled when training neural networks. Should one take them into account when designing the neural network architecture, or should one just trust the neural networks to find them? In this talk, I will present a framework in which these questions can be naturally addressed. We will see that the geometry of the neural network architecture will dictate how it will react to symmetries in the data.

This talk is based on joint work with Fredrik Ohlsson and Oskar Nordenfors.

2025 Friday April 25th - 14.05

Title: Predicting interactions in dynamic networks with distributed adaptive stochastic gradient optimization

Speaker: Martin Rosvall, IceLab/Physics, UmU

Abstract: Predicting future interactions or novel links in networks is an indispensable tool with many applications across diverse domains, including drug repurposing based on genetic networks, money laundering detection in financial systems, and recommendation systems using transactional data. Among the many techniques developed for link prediction, those leveraging the networks' community structure have proven highly effective. For example, the recently proposed MapSim predicts links based on a similarity measure derived from the code structure of the map equation, an information-theoretic community-detection objective function that operates on network flows. The map equation benefits from Infomap, its fast optimization method widely regarded as one of the best network-clustering algorithms. However, we developed Infomap for static networks. While its stochastic greedy search algorithm excels at identifying reliable communities in network snapshots, Infomap cannot effectively integrate new data or adapt to smooth transitions over time in continuously evolving relational networks. This shortcoming raises a computational challenge: How can we equip the map equation framework with a computationally efficient optimization method to enable adaptive analysis of dynamic networks, leveraging evolving relational data to predict future interactions and uncover novel links in real time?

2025 Friday April 4th - 13.00 

Title: Data-driven construction of basis sets and atomic potentials

Speaker: Valera VeryazovLinks to an external site., Lunds Universitet

Abstract: The traditional approach to constructing atomic basis sets and model potentials is based on atomic calculations and energy minimization. This project, now sponsored by eSSENCE, explores an alternative strategy:
replacing energy minimization with the minimization of the difference between computed and reference electron density. The optimization of parameters used in the basis sets and in atomic potentials is performed using machine learning techniques.

2025 Friday March 28th - 14.05

Title: Structural Rigidity Using Combinatorics and Group Theory

Speaker: Klara Stokes, Mathematics and Mathematical Statistics, UmU

Abstract: Structural rigidity is the study of when a structure made of fixed-length bars and flexible joints holds its shape or can move. This area lies at the crossroads of geometry and combinatorics and traditionally uses tools from algebra and geometry to analyze different types of structures, such as bar-joint frameworks and tensegrities. In this talk, I’ll present an alternative viewpoint—using graphs and group theory to study rigidity. By focusing on the role of symmetry and structure, this approach offers a more intuitive and flexible way to understand when and why a framework is rigid. I’ll introduce the main ideas through simple examples and explain how this perspective connects to other themes in mathematics.

2025 Friday February 21st - 14.05

Title: Topology optimization of decoupling networks for antenna arrays

Speaker: Pan Lu, Computing Science, UmU

Abstract: Near-field coupling between closely placed antennas is unavoidable, and it is a well-known challenge in designing compact systems for wireless communications. Traditional decoupling techniques usually rely on human expertise and require considerable design effort. In this work, we employ a density-based topology optimization approach to design decoupling networks for metallic antenna arrays. The design problem is formulated as a multi-objective optimization problem, including maximizing the radiated energy and minimizing the reflected energy. The antennas are replaced by their time-domain impulse responses to improve computational efficiency and enable the usage of gradient-based optimization methods. We implement an in-house 3D finite difference time domain (FDTD) solver for the time-domain Maxwell's equations, and the simulations are performed on HPC2N. We will present two design examples of the decoupling feeding network for a two-element antenna array, which are manufactured and validated experimentally.

2025 Friday February 7th - 14.05

Title: PDE Solution Operator Learning Using Energy Minimization and MLPs

Speaker: Carl Lundholm, Mathematics and Mathematical Statistics, UmU

Abstract: We develop and evaluate a method for learning solution operators to nonlinear problems governed by partial differential equations. The approach is based on a finite element discretization and aims at representing the solution operator by an MLP that takes latent variables as input. The latent variables will typically correspond to parameters in a parametrization of input data such as boundary conditions, coefficients, and right-hand sides. The loss function is most often an energy functional and we formulate efficient parallelizable training algorithms based on assembling the energy locally on each element. For large problems, the learning process can be made more efficient by using only a small fraction of randomly chosen elements in the mesh in each iteration. The approach is evaluated on several relevant test cases, where learning the solution operator turns out to be beneficial compared to classical numerical methods.

The work is a collaboration with Mats G. Larson, Anna Persson, Erik Burman, and Karl Larsson.

2025 Friday January 24th - 14.00

Title: Advanced Learning for Machine Automation

Speaker: Prof. Reza GhabchelooLinks to an external site., Tampere University

Abstract: Reza is professor in autonomous mobile machines at Tampere University, Faculty of Engineering and Natural Sciences, unit Automation Technology and Mechanical Engineering.

2024

Friday Sept.6 2024, 14:05

Title: Real-time sonification of processes and activities of parallel computers

Speaker: Prof. Marco Alunno (Universidad EAFIT, Colombia)

Abstract:Developers of parallel algorithms must repeatedly debug and assess the efficiency of their codes. For this, they already have tools at their disposal, such as log files and several kinds of visualization techniques. Sonification, instead, as a way of "giving voice" to algorithmic calculations is a strategy that has been traditionally overlooked. Nonetheless, it is an effective form of conveying information and, like visualization, can be executed in real time, whereas other monitoring methods can be performed only post-mortem.

We are aiming at creating an algorithm for the sonification of parallel processes within a supercomputer as a tool that scientists can use along with other forms of debugging. Since sonification is made for human appreciation and humans have aesthetic inclinations and specific perceptual characteristics, the act of sonifying cannot neglect the importance of the acoustic pleasantness (however this is defined), if it expected to be of some help to its listeners, or have listeners at all.

At the same time, what is informative and what is pleasant are not univocal concepts; they must be negotiated in an experimental setting where different sonic options can be listened to, appraised and discussed.

2024 Friday June 14th - 14.05  

Title: Microstructural resolved simulations for Sodium ion batteries

Speaker: Paul Maidl, Institute of Electrochemistry, University Ulm, Germany (paul.maidl@dlr.de)

Abstract: Sodium ion batteries offer the chance to more sustainable cell chemistries then their Lithium counterpart, but they typically come with a reduced energy density. For the overall cell performance the porous microstructure plays an important role since it defines the pathways for the major transport processes. In addition the interface between active material and electrolyte shows a complex but critical behavior, that is not yet fully understood. Modeling and simulation of such batteries can help to understand the underlying processes and accelerate the development of new materials.

2024 Friday June 14th - 14.05  

Title: Microstructural resolved simulations for Sodium ion batteries

Speaker: Paul Maidl, Institute of Electrochemistry, University Ulm, Germany (paul.maidl@dlr.de)

Abstract: Sodium ion batteries offer the chance to more sustainable cell chemistries then their Lithium counterpart, but they typically come with a reduced energy density. For the overall cell performance the porous microstructure plays an important role since it defines the pathways for the major transport processes. In addition the interface between active material and electrolyte shows a complex but critical behavior, that is not yet fully understood. Modeling and simulation of such batteries can help to understand the underlying processes and accelerate the development of new materials.

2024 Friday May 24th  - 14.05  

Title: Synthesizing multi-log grasp poses

Speaker: Arvid Fälldin, Department of Physics, Umeå University

Abstract: Multi-object grasping is a challenging task. It is important for energy and cost-efficient operation of industrial crane manipulators, such as those used to collect tree logs off the forest floor and onto forest machines. In the presented work, we used synthetic data from multibody dynamics simulations to explore how data-driven modeling can be used to infer multi-object grasp poses from images. We showed that convolutional neural networks can be trained specifically for synthesizing multi-object grasps. Using RGB-Depth images and instance segmentation masks as input, a U-Net model outputs grasp maps with corresponding grapple orientation and opening width. Given an observation of a pile of tree logs, the model can synthesize and rate the possible grasp poses and select the most suitable one, with the possibility to respect changing operational constraints such as lift capacity and reach. When tested on previously unseen data, the proposed model found successful grasp poses with an accuracy of 95%.

2024 Tuesday April 23rd   - 14.05  

Title: A high order boundary scheme to simulate a complex moving rigid body under the impingement of a shock wave

Speaker: Yan Jiang, School of Mathematical Sciences, University of Science and Technology of China

Abstract: In this talk, we study a high order numerical boundary scheme for solving the complex moving boundary problem on a fixed Cartesian mesh, and numerically investigate the moving rigid body with the complex boundary under the impingement of a shock wave. This boundary treatment can achieve high order accuracy, and has a unified form for pure convection, convection-dominated, convection-diffusion, diffusion-dominated and pure diffusion cases. Thus, it can be used for the compressible Euler equations and Navier-Stokes equations and further utilized for problems involving interactions between inviscid/viscous shocks and moving rigid bodies.

2024 Friday April 5th  - 14.05  

Title: Topology Optimization of Transitional Flows

Speaker: Harrison Nobis, Department of Mechanics, KTH (will join us at UMU soon)

Abstract: Whether considering the transport of a fluid through a pipe or the locomotion of a vehicle through a fluid, maintaining a laminar flow regime can significantly reduce the required power compared to that of a turbulent regime. We discuss how topology optimization can be utilised to uncover novel surface structures capable of delaying the onset of turbulence. The methodology relies on gradient descent algorithms coupled with the adjoint variable method to compute sensitivity information. This methodology has been applied to the design of miniature vortex generators that could be mounted on an aircraft in order to delay the transition to turbulence and reduce skin friction drag.

2024 Friday Mar 15 - 14.05  

Title: Monte Carlo Simulations of Rarefied Atmospheres

Speaker: Philip Varghese, Oden Institute and Department of Aerospace Engineering & Engineering Mechanics, The University of Texas at Austin

Abstract: Our group at The University of Texas at Austin has developed the PLANET code based on the Direct Simulation Monte Carlo (DSMC) method to model rarefied atmospheres. Solution of the Boltzmann equation via statistical simulation is a powerful technique to compute gas flows at low densities when the Navier-Stokes equations fail. This will be illustrated with a number of examples including 3-D simulations of the volcanic atmosphere of Jupiter’s moon Io, and the Pluto-Charon system.

Bio-sketch: Prof. Varghese holds the Ernest H. Cockrell Centennial Chair in Engineering and is the Director of the Center for Aeromechanics Research at UT Austin. His research focuses on understanding the basic molecular processes occurring in high speed and high temperature, and non-equilibrium flows. This is an inter-disciplinary field, requiring a synthesis of physics and chemistry with the more traditional engineering disciplines of fluid mechanics, heat transfer, and thermodynamics. He applies his work to the study of hypersonic and rarefied flows, plasmas, and combustion.

He was a Fulbright Senior Scholar in France in 1993. He received the Lockheed Martin Aeronautics Company Award for Excellence in Engineering Teaching in Spring 2003 and was elected to the Academy of Distinguished Teachers at the University of Texas in 2005. In February 2012 he was selected Professor of the Year by the UT Senate of College Councils and was awarded The University of Texas System Regents’ Outstanding Teaching Award in August 2016.

2024 Friday Mar 1 - 14.05  

Title: Autocalibration of multibody dynamics models - Are we there yet?

Speaker: Martin Servin, Department of Physics, Umeå University

Abstract: With a contacting multibody dynamics you can do physics-informed planning and control of mobile manipulators and vehicles with consideration to energy-efficiency and safety. The dynamics model can serve both estimation of the current state and prediction of future states, given some plan and control inputs. The horizon you can optimize over depends on the computational speed of the model and how accurately it captures the dynamics of the real system. What does it mean to calibrate a complex dynamics model of a vehicle or manipulator? What alternative methods are there? Can this process be automated? I will try to answer these questions, having in mind a forestry machine simulator that we are currently working on.

2024 Friday Feb 16 - 14.05  

Title: Time-Domain Topology Optimization of Arbitrary Dispersive Materials for Broadband 3D Nanophotonics Inverse Design

Speaker: Emad Hassan, Applied Physics and Electronics, Umeå University

Abstract: Nanostructures have unlocked myriads of functionalities in nanophotonics by engineering light–matter interaction beyond what is possible with conventional bulk optics. The space of parameters available for design is practically unlimited due to the large variety of optical materials and nanofabrication techniques. Thus, computational approaches are necessary to efficiently search for the optimal solutions. In this work, we enable the free-form inverse design in 3D of linear optical materials with arbitrary dispersion and anisotropy. This is achieved by (1) deriving an analytical adjoint scheme based on the complex-conjugate pole-residue pair model in the time domain and (2) its implementation in a parallel finite-difference time-domain framework with a topology optimization routine, efficiently running on high-performance computing systems. Our method is tested on the design problem of field confinement using dispersive nanostructures. The obtained designs satisfy the fundamental curiosity of how free-form metallic and dielectric nanostructures perform when optimized in 3D, also in comparison to fabrication-constrained designs. Unconventional free-form designs revealed by computational methods, although may be challenging or unfeasible to realize with current technology, bring new insights into how light can more efficiently interact with nanostructures and provide new ideas for forward design.

2024 Friday, Feb 2 - 14.05 

Title: Computing formation enthalpies through an explainable machine learning method: the case of Lanthanide Orthophosphates solid solutions

Speaker: Edoardo Di Napoli, Forschungszentrum Jülich 

Abstract: In the last decade, the use of Machine and Deep Learning (MDL) methods in Condensed Matter physics has seen a steep increase in the number of problems tackled and methods employed. A number of distinct MDL approaches have been employed in many different topics; from prediction of materials properties to computation of Density Functional Theory potentials and inter-atomic force fields. In many cases the result is a surrogate model which returns promising predictions but is opaque to the inner mechanisms of its success. On the other hand, the typical physicist looks for answers that are explainable and provide a clear insight on the mechanisms governing a physical phenomena. In this work, we describe a proposal to use a combination of traditional Machine Learning methods to obtain an explainable model that outputs an explicit functional formulation for the material property of interest. We demonstrate the effectiveness of our methodology in deriving a new expression for the enthalpy of formation of solid solutions of lanthanide orthophosphates that goes beyond the known first order approximation.

2023 Friday, Dec 1 - 14.05  

Title: Numerical solutions for elastic wave equations in layered media with perfectly matched layers

Speaker:  Balaje Kalyanaraman, Department of Mathematics and Mathematical Statistics

Abstract: The elastic wave equation governs seismic waves arising from earthquakes and other seismic events. Numerical techniques are required to simulate the wave propagation due to the difficulty of obtaining analytical solutions, especially in real-life scenarios. However, the elastic wave equations arising in such applications are formulated in large/infinite domains, and therefore, the computational domain needs to be restricted to save computational costs. A perfectly matched layer (PML) is an absorbing layer of finite thickness that effectively absorbs all the incoming waves without reflections and thus makes it appropriate for truncating the domain. In this talk, I will discuss the system of PDEs that govern the wave propagation on elastic media with perfectly matched layers. I will then solve the PDE using the summation-by-parts (SBP) finite difference method to demonstrate the stability of perfectly matched layers along with some real-life applications.

2023

2023 Friday, Nov 24 - 14.05  

Title: Revealing Biophysical Processes Through Computational Simulations

Speaker:  Pedro Ojeda May, HPC2N, Umeå University

Abstract: In this talk, we will go over different methods that are used to simulate dynamical trajectories of Biophysical systems, for instance, classical and quantum mechanical methods. To achieve time-scales in the simulations that are comparable with experiments several optimizations are employed, and we will explore some of the strategies in this area. Applications of simulations to Biophysical systems will also be discussed.

2023 Friday, Nov 10 - 14.05  

Title: Microwave imaging for medical applications

Speaker:  Pan Lu, Department of Computing Science, Umeå University

Abstract: Microwave imaging is a method using microwaves to recover information of targets inside an investigated region. It has potential to be used as an alternative technique for medical applications such as breast cancer detection and stroke detection, as microwaves are non-ionizing and harmless to humans. Microwave tomography (quantitative microwave imaging) aims to reconstruct the dielectric properties of a region by solving an electromagnetic inverse scattering problem, including solving a forward wave propagation problem and an inverse linear system. In this seminar, I will present our approach based on the distorted Born iterative method, which uses finite difference time domain method as the forward solver and fast iterative shrinkage/thresholding algorithm as the inverse solver. Numerical and experimental results of simple models and complex models will be presented.

2023 Friday, Sep 13 - 14.05  

Title: Data-driven models for optimizing sequential action of a wheel loader

Speaker: Koji Aoshima, Department of Physics

Abstract: A wheel loader is a construction/mining machine which is used for the task of repeated loading of soil from a pile to dump trucks. We aim to maximize the total performance of a sequence of loading actions for fully or semi-automated machines. The difficulty lies in that the pile shape is changed by every loading action while the performance of a loading action is affected by the pile shape. Therefore, a greedy strategy of always choosing the loading action that maximizes the performance for the immediate loading might be sub-optimal over a longer horizon. In this seminar, we present a data-driven method for predicting the outcome of a sequence of loading actions given the initial pile shape. The outcome includes the loaded mass, time, work, and the resulting pile shape. We trained deep neural networks from 10,000 loading simulations to predict the performance and the resulting pile shape. The models enable rapid evaluation of sequential loading plans in the search for near-optimal plans.

2023 Friday, Sep 15 - 14.05  

Title: Processing and visualisation of Ionospheric data

Speaker: Juan C. Araújo, Department of Science and Mathematics Education

Abstract: Incoherent scatter radar (ISR) techniques provide reliable measurements for the analysis of ionospheric plasma. Measurements of electron and ion densities, temperatures, and line-of-sight velocities are derived by employing antennas that transmit and receive radio waves. Recent developments in ISR technologies are capable of generating high-resolution volumetric data from multiple beam measurements. Examples of such technologies employ the so-called phased array antennas like the AMISR in North America or the upcoming EISCAT_3D in the northern Fennoscandia region. Traditional visualization methods, for example, 2D projections, applied to volumetric images render a reduced set of the available data and important aspects of the data may be lost to the analyst.

We present an interactive approach for the exploration and visualization of spatio-temporal and volumetric ionospheric data. The strategy is targeted at offering the analyst a wider range of alternatives in order to interpret ISR data. The proposed novel strategy allows for the reconstruction of ionospheric volume images by means of a novel sparse interpolation algorithm tailored for the particular features of ISR data. The interpolation offers estimation of gradients and processing of the challenging case of missing data. The reconstructed image is output by using volume rendering combined with customizable

2023 Wednesday, May 17 - 3.15pm  

Title: Cut FEM meets Finite Differences

Speaker:  Gunilla Kreiss, Uppsala University

Abstract: There is a cut-FEM methodology with ghost penalty stabilization, which can be applied to hyperbolic conservation laws. Explicit time-stepping is preferable for hyperbolic problems, but even the standard DG and CG metods suffer from increasingly severe time-step restrictions as the order of the method increases. For high order finite difference methods the time-step restriction is not at all as severe. In this talk we will explore possibilities of applying the cut-FEM methodology to finite difference methods. The goal is to formulate a finite difference method that can be seen as a Galerkin method. Applying the cut-FEM methodology will then yield an immersed boundary finite difference method.

2023 Friday, April 21 - 14.05  

Title: Matrix Chain Multiplications and Temporary Storage

Speaker: Lars Karlsson, Department of Computing Science

Abstract: The arithmetic cost of a matrix chain multiplication such as ABC varies with the parenthesization of the expression. Depending on the sizes of the matrices, either (AB)C or A(BC) minimizes the arithmetic cost. The number of parenthesizations grows exponentially in the length of the chain. Finding an optimal parenthesization is a classic problem, often used as a textbook example of dynamic programming, for which fast optimal and approximate algorithms are known. What is considerably less well understood, however, is the temporary storage aspect of the problem, especially when each multiplication is performed using an efficient out-of-place routine (e.g., xGEMM in the BLAS library). Temporary storage is needed to hold intermediate products. In this talk, I will present an ongoing investigation of how to evaluate matrix chains with a minimum of temporary storage. I seek optimal algorithms that are fast enough for practical use on short matrix chains, since both compilers and interpreters of linear algebra expressions encounter the temporary storage problem. Experiments indicate that the arithmetic cost and temporary storage can often, but not always, be simultaneously minimized.

2023 Friday, March 3 - 14.05  

Title: Anapole plasmonic meta-atom enabled by inverse design for metamaterials transparency

Speaker: Emad Hassan, Department of Applied Physics and Electronics

Abstract:  Anapole states are broadly investigated in nanophotonics for their ability to provide field enhancement and transparency. While low extinction has been achieved in dielectric nanoparticles due to the absence of intrinsic losses, in the case of plasmonic nanostructures this is still lacking. Here, we report an easy-to-fabricate planar plasmonic nanostructure found via topology optimization, which exhibits an anapole state with close-to-ideal characteristics in the visible regime including weak absorption, high near-field enhancment, and strong suppression of scattering. The nanonantenna can act as an individual meta-atom because, due to low inter-coupling, it preserves its optical response even when used in highly packed metasurfaces and metamaterials.

2023 Friday, January 27 - 14.05  

Title: Reliable and sustainable computations: a way forward

Speaker:  Roman Iakymchuk, Department of Computing Science.  

Abstract: In this talk, I present my work on accuracy and reproducibility assuring strategies for parallel iterative solvers that may not hold due to the non-associativity of floating-point operations. These strategies primarily rely on guarding every bit of result until the final rounding, hence they can be costly. The energy consumption constraint for large-scale computing encourages scientists to revise the architecture design of hardware but also applications, algorithms, as well as the underlying working/ storage precision. The main aim is to make the computing cost sustainable and apply the lagom principle (''not too much, not too little, the right amount"), especially when it comes to working/ storage precision. Thus, I will introduce an approach to address the issue of sustainable, but still reliable, computations from the perspective of computer arithmetic tools; re-design of algorithms and high performance applications with low and mixed precision; but also novel ways of rounding numbers like stochastic rounding and the probabilistic (aka optimistic) error analysis, which is more realistic and closely captures the actual computed errors.

2023 Friday, January 13 - 15.05  

Title: How accurate does Newton have to be?

Speaker:  Carl Christian Kjelgaard Mikkelsen, Department of Computing Science.  Joint work with Lorién López-Villellas and Pablo García-Risueño

Abstract: We analyze the convergence of quasi-Newton methods in exact and finite precision arithmetic. In particular, we derive an upper bound for the stagnation level and we show that any sufficiently exact quasi-Newton method will converge quadratically until stagnation. In the absence of sufficient accuracy, we are likely to retain rapid linear convergence. We confirm our analysis by computing square roots and solving bond constraint equations in the context of molecular dynamics. We briefly discuss implications for parallel solvers.

2023 Friday, January 10 - 14.05  

Title: Learning terrain trafficability from simulation and laser-scanned terrains

Speaker: Erik Wallin and Martin Servin, Department of Physics

Abstract: We present a method that uses high-resolution topography data of rough terrain and ground vehicle simulation to predict trafficability. Trafficability is expressed as three independent measures: the ability to traverse the terrain at a target speed, energy consumption, and acceleration. The measures are continuous and reflect different objectives for planning that go beyond binary classification. A deep neural network is trained to predict the trafficability measures from the local heightmap and target speed. With an inference speed 3000 times faster than the ground truth simulation and trivially (?) parallelizable, the model is well suited for trafficability analysis and optimal route planning over large areas. Applications to optimization in forestry is discussed.

2022

2022 Friday, December 16 - 15.05  

Title: Reliable and sustainable computations: a way forward

Speaker: Roman Iakymchuk, Department of Computing Science

Abstract: In this talk, I present my work on accuracy and reproducibility assuring strategies for parallel iterative solvers that may not hold due to the non-associativity of floating-point operations. These strategies primarily rely on guarding every bit of result until the final rounding, hence they can be costly. The energy consumption constraint for large-scale computing encourages scientists to revise the architecture design of hardware but also applications, algorithms, as well as the underlying working/ storage precision. The main aim is to make the computing cost sustainable and apply the lagom principle (''not too much, not too little, the right amount"), especially when it comes to working/ storage precision. Thus, I will introduce an approach to address the issue of sustainable, but still reliable, computations from the perspective of computer arithmetic tools; re-design of algorithms and high performance applications with low and mixed precision; but also novel ways of rounding numbers like stochastic rounding and the probabilistic (aka optimistic) error analysis, which is more realistic and closely captures the actual computed errors.

2022 Friday, December 2 - 15.05  

Speaker: Karl Larsson, Department of Mathematics and Mathematical Statistics.

Title: Discrete extension for unfitted finite element methods

Speaker: Karl Larsson, Department of Mathematics and Mathematical Statistics.

Abstract: In an unfitted finite element method, the computational grid does not match the problem domain, which
leads to the possibility of an approximation space containing very small basis functions in the sense that they
are non-zero on a very small part of the domain. As a result, the degrees of freedom associated with very small
basis functions are ill-conditioned, and basic stability properties of the approximation space cannot be guaranteed.

In this talk, I will present an approach where the problematic small basis functions are coupled with large basis
functions. This is based on extending the solution on elements with a large intersection with the domain to elements
with a small intersection with the domain. Optimal order interpolation is preserved while giving us the stability we need.

In practice, the extension is applied via a simple matrix transformation of the linear system of equations. In contrast to
other approaches for unfitted finite element methods, there is no need for adding stabilization terms to the weak form of
the problem. Hence, it can be applied to existing codes with minimal effort.

2022 Friday, November 18 - 15.05  

Title: AMITIS: A 3D GPU-Based Hybrid-PIC Model for Space and Plasma Physics

Speaker: Shahab Fatemi, Department of Physics, Umeå University.

Abstract: We have developed, for the first time, an advanced modeling infrastructure in space simulations (AMITIS) with an embedded three-dimensional self-consistent grid-based hybridmodel of plasma (kinetic ions and fluid electrons) that runs entirely on graphics processing units
(GPUs). The model uses NVIDIA GPUs and their associated parallel computing platform, CUDA, developed for general purpose processing on GPUs. The model uses a single CPUGPU pair, where the CPU transfers data between the system and GPU memory, executes CUDA kernels, and writes simulation outputs on the disk. All computations, including movingparticles, calculating macroscopic properties of particles on a grid, and solving hybrid model equations are processed on a single GPU. We explain various computing kernels within AMITIS and compare their performance with an already existing well-tested hybrid model of plasma that runs in parallel using multi-CPU platforms. We show that AMITIS runs ∼10 times faster than the parallel CPU-based hybrid model. We also introduce an implicit solver for computation of Faraday’s Equation, resulting in an explicit-implicit scheme for the hybrid model equation. We show that the proposed scheme is stable and accurate. We examine the AMITIS energy conservation and show that the energy is conserved with an error < 0.2% after 500,000 timesteps, even when a very low number of particles per cell is used.

2022 Friday, November 4 - 15.05  

Title: How the acoustic black hole works

Speaker: Martin Berggren, Department of Computing Science, Umeå University. Joint work with Abbas Mousavi and Eddie Wadbro

Abstract: The acoustic black hole is a device characterized by broadband absorption of acoustic waves. Mironov introduced in 1988 such a device in the form of a beam whose cross-sectional area gradually tapers off to zero. The speed of propagation of transversal waves in such a beam will then successively be reduced to zero, and the waves will never reach the end of the beam — ideally. However, for the device to work in practice, a small amount of damping material needs to be added towards the end of the beam. Such a device can be used to minimize the amount of damping materials needed to obtain efficient broadband structural vibration damping of various machinery. About 20 years ago, Mironov proposed a similar idea targeted to sound waves in air and suggested a design concept to accomplish the black-hole effect. Also here, the idea is to slow down the speed of propagation, but now for pressure waves in a waveguide and to absorb the waves by a small amount damping material placed at the end of the waveguide. Experimental results indeed confirm that the device works as an absorber. However, a puzzling conclusion from the experiments is that the addition of damping material towards the end of the device has essentially no effect, in contrast to what was expected. We have investigated through numerical simulations the effects of various possible damping mechanisms that may occur in the device. The conclusion from the simulations is that the mechanisms that cause the (weak) black-hole effect in the waveguide is quite different from the one originally intended by Mironov.

2022 Friday, October 21 - 15.05  

Title: FLOPs as a Discriminant for Dense Linear Algebra Algorithms

Speaker: Francisco López Sánchez, Department of Computing Science, Umeå University

Abstract: Linear algebra expressions are commonly evaluated through a sequence of invocations to highly optimised kernels provided in libraries such as the Basic Linear Algebra Subroutines (BLAS) and Linear Algebra PACKage (LAPACK). A sequence of kernels represents an algorithm and, in general, because of associativity, algebraic identities, and multiple kernels, one expression can be evaluated via many different algorithms. These, while all mathematically equivalent (i.e., in exact arithmetic, they all compute the same result), often differ noticeably in terms of execution time. When faced with a decision, high-level languages, libraries, and tools such as Julia, Armadillo, and Linnea choose by selecting the algorithm that minimises the floating-point operation (FLOP) count. In this talk, we will discuss the validity of the FLOP count as a discriminant for dense linear algebra algorithms. 

To test the validity of the FLOP count as a discriminant in this context, we focused on analysing anomalies: problem instances for which the fastest algorithm does not perform the least number of FLOPs. To do so, we focused on relatively simple expressions and analysed when and why anomalies occurred. We found that anomalies exist and tend to cluster into large contiguous regions in the problem space. We concluded that FLOPs is not a sufficiently dependable discriminant even when building algorithms with highly optimised kernels.

2022 Friday, October 7 - 15.05  

Title: 2D modelling of lake primary production

Speaker: Hugo Harlin, IceLab / Department of Ecology and Environmental Sciences, Umeå University

Abstract: Process-based modelling has yielded valuable insight into the interplay of fundamental physical processes with the biogeochemistry of primary production and nutrient recycling in lakes. The vast majority of this research has focused on algae living suspended in the water, so-called pelagic algae, using 1D models.

In contrast, benthic algae that live along the lake bottom have rarely been included in these models, in part because 1D models restrict benthic algae to a single depth. Overcoming this limitation, we have developed a 2D model, formulated as a system of PDE, to explore the impact of physical lake properties such as size, morphometry, and mixing on the competitive interaction between benthic and pelagic algae.

2022 Friday, September 23 - 15.05  

Title: Representability of multiscale physics in Graph Networks

Speaker: Hannes Marklund, Department of Physics, Umeå University

Abstract: A Graph Neural Network (GNN) is an optimizable model that transforms attributes of a graph such that the permutation symmetry is respected. A GNN can be used to represent physical systems with an exploitable graph structure. By learning from data, the model can be used for system identification, model discovery, inverse dynamics, forward dynamics, and more. 

A traditional message-passing GNN has been implemented with the motivation of testing how well it can learn to represent and simulate low-dimensional multiscale mechanical systems. This ability turns out to be limited for the investigated systems. We suggest that the problem stems from the fact that information propagates one step per iteration. This presentation will serve as a chance to introduce myself and some of the topics I am interested in. 

The presentation will mainly cover my master thesis, and I will end by introducing my current research.

2022 Friday, September 9 - 15.05  

Title: Topology Optimization in Visco-thermal Acoustics

Speaker: Abbas Mousavi, Department of Computing Science, Umeå University

Abstract: Topology optimization is a process to determine the optimal layout and connectivity of material inside a design domain. The most common approach to solve topology optimization problems is to use the material distribution method. In this method, a so-called material indicator function represents the presence/absence of material inside the domain. To use this approach for boundary-effect-dominated problems, we need to identify the boundaries of the design at each iteration and compute the contribution of the boundary terms to the governing equations. To this end, we introduce a new approach by defining a boundary indicator function on the mesh faces (edges in 2D and facets in 3D). 

Acoustic waves audible to the human ear are termed sound waves. In a typical problem of propagation of sound waves, the aim is to find the distribution of the acoustic pressure in the domain. This requires solving the compressible Navier–Stokes equations, a set of complicated coupled partial differential equations involving pressure, density, particle velocity, and temperature. In most applications, we may neglect the losses, which (together with some other assumptions) simplifies the governing equations to a single equation for the pressure, known as the Helmholtz equation. However, in cases where the studied device is acoustically small (e.g., hearing-aid devices, headsets, acoustic absorbers), the so-called visco-thermal losses happening in a boundary layer close to the solid walls are non-negligible. Thus, visco-thermal acoustics is an example of boundary-effect-dominated problems.

Here we present a density-based topology optimization formulation considering the boundary indicator approach for a couple of problems in visco-thermal acoustics.

2022 Friday June 17 - 10.05

Title: Parallel and Scalable Solution of the Helmholtz Equation via Wave Equation Iteration

Speaker: Daniel Appelö, Michigan State University

Abstract: We introduce a novel idea, the WaveHoltz iteration, for solving the Helmholtz equation. Our method makes use of time domain methods for wave equations to design frequency domain Helmholtz solvers. We show that the WaveHoltz iteration we propose results in a symmetric and positive definite linear system even though we are solving the Helmholtz equation. As our method utilizes time-domain solvers we can exploit features such as local timestepping that are not present in the frequency domain. A unique “free lunch” property that WaveHoltz possesses allows us to solve for multiple frequencies at the cost of a single solve. We will present numerical examples, using various discretization techniques, that show that our method can be used to solve problems with rather high wave numbers.

2022 Friday June 17 - 15.05

Title: Some computational methods for kinetic transport equations

Speaker: Yingda Cheng, Michigan State University

Abstract: Kinetic equations are mesoscale description of the transport of particles such as neutrons, photons, electrons, molecules as well as their interaction with a background medium or among themselves, and they have wide applications in many areas of mathematical physics, such as nuclear engineering, fusion device, optical tomography, rarefied gas dynamics, semiconductor device design, traffic network, swarming, etc. Because the equations are posed in the phase space (physical space plus velocity space), any grid based method will run into computational bottleneck in real applications that are 3D in physical space and 3D in velocity space. This talk will present three numerical solvers that we developed aiming at efficient computations of kinetic equations: the adaptive sparse grid discontinuous Galerkin method, the reduced basis method and the machine learning moment closure method. They aim at effective reduced order computations of such high dimensional equations. Benchmark numerical examples will be presented.

2022 Friday, June 3 - 15.05  

Title: A Space-Time CutFEM on Overlapping Meshes

Speaker: Carl Lundholm, Department of Mathematics and Mathematical Statistics, Umeå University

Abstract: We present a cut finite element method for the heat equation on two overlapping meshes. By overlapping meshes we mean a mesh hierarchy with a stationary background mesh at the bottom and an overlapping mesh that is allowed to move around on top of the background mesh. Overlapping meshes can be used as an alternative to costly remeshing for problems with changing geometry. In this work the overlapping mesh is prescribed a simple continuous mesh movement, meaning that its location as a function of time is continuous and piecewise linear. For the discrete function space, we use continuous Galerkin in space and discontinuous Galerkin in time, with the addition of a discontinuity on the boundary between the two meshes. The finite element formulation is based on Nitsche's method and also includes an integral term over the space-time boundary that mimics the standard discontinuous Galerkin time-jump term. The continuous mesh movement results in a space-time discretization for which standard analysis methodologies either fail or are unsuitable. We therefore propose a new energy analysis framework that is general and robust enough to be applicable to the current setting. The main result of the energy analysis is an a priori error estimate that is of optimal order with respect to both time step and mesh size. We also present numerical results for a problem in one spatial dimension that verify the analytic error convergence orders.

2022 Friday April 8 - 15.05 

Title: Digital Physics - An overview

Speaker: Martin Servin, Department of Physics, Umeå University

Abstract: Digital physics is the art and science of creating virtual environments that evolving according to the laws of physics, often in realtime. This enables experiments with machines and robots that do not yet exist and creation of synthetic training data for developing AI-based control and perception. I will give a brief overview of the research group, our scientific questions, and computational methods. Some example applications will be highlighted - involving vehicles and robots that traverse rough terrain, dig, load,  and transport granular media.

2022 Friday May 20 - 15.05  

Title: Time-domain topology optimization of wideband dispersive plasmonic nanostructures

Speaker: Emadeldeen Hassan, Department of Applied Physics and Electronics, Umeå University

Abstract: Topology optimization techniques enabled the inverse design of nanophotonic structures for desired optical properties. So far, these techniques have been proposed to optimize dielectric integrated optical circuits and nanostructures using frequency-domain methods. However, the dispersive properties of plasmonic nanostructures indicate that a time-domain formulation is more efficient for simulating or optimizing such problems. In this talk, I will present a new gradient-based topology optimization approach to design wideband dispersive plasmonic nanoantennas. The method is formulated based on the time-domain Maxwell’s equations with the Drude model used to describe the metal’s dispersion. The interpolation between metallic and dielectric media causes high-field localization associated with plasmonic effects, which leads to poor convergence of the optimization routine. To relax this issue, we introduce artificial damping in Maxwell’s equations that suppresses the undesired field localization and guarantees convergence. Several novel designs of 2D and 3D nanostructures capable of boosting the enhancement/focusing of the electric energy at a specified domain of interest will be presented.

2022 Friday May 13 - 15.05  

Title: Scalable Semidefinite Programming

Speaker: Alp Yurtsever, Department of Mathematics and Mathematical Statistics, Umeå University

Abstract: Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. In this work, we develop a provably correct randomized algorithm for solving large, weakly constrained SDP problems by economizing on the storage and arithmetic costs. The key insight is maintaining only a small sketch of the decision variable. Combining this idea with the conditional gradient methods, we introduce an algorithm that can solve very large SDPs that are not accessible to other convex optimization methods. Numerical evidence shows that the method is effective for a range of applications, including relaxations of MaxCut, phase retrieval, and quadratic assignment. - This is a joint work with Joel Tropp, Olivier Fercoq, Madeleine Udell, and Volkan Cevher.

2022 Friday May 6 - 15.05  

Title: The summation-by-parts finite differences

Speaker: Siyang Wang, Department of Mathematics and Mathematical Statistics, Umeå University

Abstract: Wave propagation can be modeled by time-dependent hyperbolic partial differential equations. Efficient and reliable simulation of wave propagation requires stable and high-order accurate numerical methods. In the finite difference framework, it is often challenging to derive a method that is both stable and high-order accurate for problems with physical boundaries, material interfaces and complex geometry. In this seminar, I will discuss the summation-by-parts concept that serves as a recipe for deriving provably stable and high-order spatial discretization for wave propagation problems. 

2020

26.02.2020, 14:15-15:00, MC313: Kostas Zygalakis, The University of Edinburgh, Bayesian inverse problems, prior modelling and algorithms for posterior sampling

2019

03.12.2019, Jonathan Vallin, Analysis of a Deep One Unit Residual Network

18.11.2019, 15:15-16:00, MA346: Marcus Grote, University of Basel,
High-Order Explicit Local Time-Stepping Methods For Wave Propagation

2018

12.04.2018, 14:00-15:00, MA356, Andrii Dmytryshyn, Umeå University, Generic matrix polynomials with fixed rank and fixed degree

2017

13.12.2017, 14:00-15:00, MA346, André Massing, Umeå University, A stabilized cut discontinuous Galerkin framework
22.11.2017, 14:00-15:00, MA346: Eddie Wadbro, Umeå University, On mathematical morphology, non-linear filters, and length scale control in topology optimization
06.11.2017, 14:00-15:00, MA356: Kristin Kirchner, Chalmers University of Technology, Strong and weak convergence of numerical methods for fractional SPDEs with spatial white noise
01.11.2017, 15:00-16:00, MA346: Jianbo Cui, Chinese Academy of Sciences Beijing, Strong convergence rate of a splitting fully discrete scheme for stochastic nonlinear Schrödinger equation
01.11.2017, 14:00-15:00, MA346: Jialin Hong, Chinese Academy of Sciences Beijing, Stochastic symplectic methods and stochastic multi-symplectic methods
01.11.2017, 11:00-11:45, MA176: Jialin Hong, Chinese Academy of Sciences Beijing, Presentation of the Academy and the Institute of Computational Mathematics
15.05.2017, 14:00-15:00, MA136: Patrick Henning, KTH Stockholm, Finite element discretizations for nonlinear Schrödinger equations with rough potentials
04.05.2017, 14:00-15:00, MA146: Mats G Larson, Umeå University, Finite Elements for PDEs on Surfaces
27.04.2017, 14:00-15:00, MA346: Anna-Karin Tornberg, KTH Stockholm, Highly accurate integral equation based methods for surfactant laden drops in two and three dimensions
31.03.2017, 15:15-16:00, Umit Lounge: Stefano Giani, Durham University, High-Order/hp-Adaptive Multilevel Discontinuous Galerkin Methods
30.03.2017, 15:15-16:00, Umit Lounge: Luka Grubišić, University of Zagreb, Mesh independent convergence rates for the FEAST algorithm applied to self-adjoint operators

2016

30.08-02.09.2016: Michael Tretyakov, University of Nottingham, Mini-course on numerical methods on SDEs

2015

02.10.2015, 11-12, N340, Guillaume Dujardin, Indria Nord-Europe, High order exponential integrators for rotating Bose-Einstein condensates
04.06.2015, 11-12, MA356, Xiaojie Wang, Central South University, Changsha, Strong convergence rates for numerical approximations of semi-linear parabolic stochastic partial differential equations with additive noise
21.04.2015, 11-12, MA356, Eskil Hansen, Lund University, Splitting of nonlinear parabolic equations
26.03.2015, 09-10, MA146, Mats G. Larson, Umeå University, Cut finite elements for PDEs on surfaces
10.02.2015, 11-12, MA146, Luka Grubišić, University of Zagreb, Low rank techniques for infinite-dimensional Lyapunov equations and applications

2014

04.12.2014, 11-12, MC323, Olof Runborg, KTH Stockholm, Fast Interface Tracking Using Multiresolution Representations of Curves and Surfaces
24.11.2014, 11-12, MA346, Per Lötstedt, Uppsala Universitet, Stochastic simulation with diffusion in molecular biology
27.08.2014, 14-15, MA136, Elias Jarlebring, KTH Stockholm, On the infinite Arnoldi method for nonlinear eigenvalue problems
09.06.2014, 14-15, MA356, Richard Tsai, The University of Texas at Austin, Boundary integrals methods using implicitly defined interfaces
05.05.2014, 14-15, MA136, Ernst Hairer, University of Geneva, Control of parasitic solutions in linear multistep methods
27.01.2014, 10-11, MA346, Luka Grubišić, University of Zagreb, Residual estimates for Fredholm valued operator eigenvalue problems