GAMM2025

Session

S22: Scientific computing

S22

8 Apr 2025, 08:30

Lecture and Conference Centre

Conveners

S22: Scientific computing: S22.01

• Silke Glas

S22: Scientific computing: S22.02

• Silke Glas

S22: Scientific computing: S22.03

• Melina Merkel
• Andreas Sommer

S22: Scientific computing: S22.04

• Silke Glas

S22: Scientific computing: S22.05

• Melina Merkel

S22: Scientific computing: S22.06

• Melina Merkel

S22: Scientific computing: S22.07

• Sebastian Götschel
• Melina Merkel

Description

Scientific Computing is concerned with the efficient numerical solution of mathematical models from both science and engineering. The field covers a wide range of topics: from mathematical modeling over the development, analysis and efficient implementation of numerical methods and algorithms to software and finally application for the solution of complex real-world problems on modern computing systems. This interdisciplinary field combines approaches from applied mathematics, computer science and a wide range of applications in which in-silico experiments play an increasingly important role.

442. Rational Surrogate Modeling of Parametric Dynamical Systems

Ulrich Römer

08/04/2025, 08:30

We consider the frequency domain simulation of second-order linear dynamical systems, which is crucial for many applications ranging from vibroacoustics to electrical circuits. These problems are parameter-dependent, involving frequency and additional parameters to account for uncertainties. This dependence on a large number of parameters results in a very high numerical cost. To address these...

443. A parallel batch greedy algorithm in reduced basis methods

Niklas Reich

08/04/2025, 09:10

The classical (weak) greedy algorithm is widely used within model order reduction in order to compute a reduced basis in the offline training phase: Ana posteriori error estimator is maximized and the snapshot corresponding to the maximizer is added to the basis. Since these snapshots are determined by a sufficiently detailed discretization, the offline phase is often computationally extremely...

444. Towards an efficient shifted Cholesky-QR for applications in model order reduction

Maximilian Bindhak

08/04/2025, 09:30

Many model order reduction (MOR) methods rely on the computation of an orthonormal basis of a subspace onto which the large full order model is projected. Numerically, this entails the orthogonalization of a set of vectors. The nature of the MOR process imposes several requirements for the orthogonalization process. Firstly, MOR is often times performed in an adaptive or iterative manner,...

445. Stability and Error Analysis of Reduced-Order Methods Based on POD with Finite Element Solutions for Nonlocal Diffusion Problems

Yufeng Nie

08/04/2025, 09:50

In this talk, we will introduce the formulation and theoretical analysis of the reduced-order numerical method constructed by proper orthogonal decomposition (POD) for nonlocal diffusion problems with a finite range of interactions. Due to the nonlocality, the corresponding discrete systems of nonlocal models have less sparsity than those for PDEs. Given the challenges of frequently handling...

446. Discontinuous Galerkin and Trefftz methods for Model Reduction

Tobias Born

08/04/2025, 10:10

The convergence speed of linear model order reduction techniques cannot be better than the Kolmogorov N-width. The problem is that it is well-known that the Kolmogorov N-width of wave-type problems only decays slowly.

In this talk we will address the question to what extent discontinuous Galerkin Trefftz formulations of parametrized partial differential equations and its associated Trefftz...

447. The Fast Newton Transform: Interpolation in downward closed spaces reaching the optimal geometric approximation rates for Bos-Levenberg-Trefethen functions

Michael Hecht

08/04/2025, 16:30

CANCELLED
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We address the computational bottleneck that arises in solving high-dimensional problems such as 6D Boltzmann, Fokker-Planck, or Vlaslov equations, multi-body Hamiltonian systems, and the inference of governing equations in complex self-organizing systems. Specifically, the challenge lies in numerically computing function expansions and their derivatives fast, while...

448. On a multigrid solution technique for the three-dimensional incompressible Navier-Stokes equations using discretely divergence-free finite elements

Christoph Lohmann

08/04/2025, 16:50

In this talk, a geometric multigrid solution technique for the incompressible Navier-Stokes equations in three dimensions is presented, utilizing discretely divergence-free finite elements. For this purpose, a set of shape functions is constructed in an a priori manner to span the subspace of discretely divergence-free functions for the Rannacher-Turek finite element pair under consideration....

450. Preconditioning for a coupled Navier-Stokes Cahn-Hilliard model for the morphology evolution in organic solar cells

Pelin Çiloğlu

08/04/2025, 17:10

Partial differential equations are used to model the morphological evolution of printed organic solar cells, capturing the underlying complex processes. In this talk, we present a Cahn-Hilliard model that describes the dynamics of a polymer, a non-fullerene acceptor, and a solvent, coupled to the Navier-Stokes equations for the fluid's macroscopic motion. To account for solvent evaporation, we...

451. Multilevel Overlapping Schwarz Preconditioners for Fluid Problems

Stephan Köhler

08/04/2025, 17:30

Additive overlapping Schwarz Methods are iterative methods of the domain decomposition type for the solution of partial differential equations. Numerical and parallel scalability of these methods can be achieved by adding coarse levels. A successful coarse space, inspired by iterative substructuring, is the generalized Dryja–Smith–Widlund (GDSW) space. In Heinlein, Hochmuth, Klawonn (2019),...

453. Temporal Multiscale Modelling of Long-term Damage in Fluid-structure Interaction Problems

Dayron Chang Dominguez

08/04/2025, 17:50

In this work, we modelled and simulated long-term damage in a fluid-structure interaction problem under a cyclic-in-time fluid regime. A temporal multiscale technique is proposed to efficiently compute the accumulation of internal damage under prolonged periodic loading conditions. This effect eventually manifests as macroscopic defects, such as cracks, or leads to failure. The study and...

454. Neural Operator-accelerated Parallel-in-Time Methods

Sebastian Götschel

09/04/2025, 08:30

Many models in computational science and engineering are based on time-dependent partial differential equations. Hence, integration along the time axis arises as an important numerical problem in many domains. While parallelization by decomposing the spatial computational domain is an established technique, on its own it will not suffice to provide the massive degree of concurrency required by...

455. A Physics-Informed Neural Network with Generalized Finite Difference method framework for solving groundwater flow

Tsung-Han Li

09/04/2025, 08:50

This paper introduces a novel approach combining physics-informed neural networks (PINN) with the generalized finite difference method (GFDM) to solve groundwater flow equations. In recent years, with advancements in computational performance and algorithm improvements, artificial intelligence has rapidly developed and been applied to many areas. One neural network architecture that...

456. Autoencoders with CUR Decompositions for Physics-preserving Low-order Models in Fluid Flow

Yongho Kim

09/04/2025, 09:10

Model order reduction is a technique for reducing the complexity of high-dimensional systems by employing a low-dimensional parametrization of system states. It facilitates efficient computations and reduces memory requirements, albeit at the expense of decreased simulation accuracy and challenges in preserving essential system properties such as sparsity, positivity, and physical laws. Thus,...

457. Concepts and strategies for the mathematical modelling of electroplating

Stephan Daniel Schwöbel

09/04/2025, 09:30

In recent years, simulation and scientific computation of electroplating processes are of growing importance to address the increasing requirements on the layer properties. In particular, the current-density and coating-thickness distributions on the electrodes are of special interest and are modelled via couplings between (quasi)static electric fields, transport processes and fluid dynamics....

458. Development of a GPU-accelerated, Finite Element based Dynamical Core for Sea Ice

Thomas Richter

09/04/2025, 09:50

Sea ice is an import part of Earth’s climate system and the accurate, large-scale simulation of sea ice dynamics remains challenging. As the development of faster processors has slowed down, a turn to more specialized hardware is needed to achieve more accurate and higher resolution simulations. Graphics processing units (GPUs) offer an order of magnitude higher floating-point performance and...

459. A Surface Crouzeix-Raviart Element for Geophysical Flow Problems

Carolin Mehlmann

09/04/2025, 16:30

This talk addresses the mathematical challenges and numerical treatment of large-scale sea-ice dynamics in climate models. The underlying model adopts a viscous-plastic framework to describe sea-ice as a two-dimensional thin layer on the ocean surface.

In the first part of the talk, we explore the formulation of the model, focusing on developing a presentation that is well-suited for modern...

460. Efficient numerical methods for the Maxey-Riley-Gatignol equation

Daniel Ruprecht

09/04/2025, 17:10

Modelling the dynamics of particles moving in a liquid is crucial for numerous applications, including marine snow aggregation in oceans and the movement of Lagrangian devices in chemical reactors. While very small particles can be accurately modeled as passive tracers, larger particles require consideration of additional forces. The Maxey-Riley-Gatignol equations (MaRGE) describe the motion...

462. Magneto-mechanical coupling for magnetostriction using isogeometric analysis

Melina Merkel

09/04/2025, 17:30

Magnetostriction refers to the deformation of magnetostrictive materials under the influence of a magnetic field, as well as the effect of mechanical stresses on their magnetic properties. These effects are important in the design of electromechanical devices, such as electric motors and transformers, where magnetostriction can lead to additional stresses, vibrations, and a reduction in the...

463. Isogeometric Analysis of 2D Magnetostatics with THB-Splines enriched by Bézier Extraction for Local Refinement

Andreas Grendas

09/04/2025, 17:50

Isogeometric Analysis (IGA) aims to enhance the seamless integration between computer-aided design (CAD) and computer-aided engineering (CAE). Local refinement is essential for efficiently resolving fine details in numerical simulations. In the context of IGA, hierarchical B-splines have gained prominence, providing an effective framework for local refinement. The work applies the methodology...

464. Algorithmic Differentiation for Second-Order Derivatives of Fixed-Point Iterations with ADOL-C

Tim Siebert

10/04/2025, 08:30

Calculating exact derivatives is a cornerstone of scientific computing. It enables deep learning, solving nonlinear partial differential equations, or asset optimization in finance. For real world applications, the calculation of derivatives poses challenges due to the complexity of the algorithms that represent the underlying function. Algorithmic Differentiation (AD) addresses this...

465. MaRDI Open Interfaces for Scientific Computing

Dmitry I. Kabanov

10/04/2025, 08:50

Modern scientific computing experiments often require the combination of multiple numerical packages, which are implemented in different programming languages. Thus, computational scientists face the task of combining these solvers together by removing the inter-language barrier via bindings or inter-process communication. Also, in cases where packages solving the same numerical problem (such...

466. Efficient Implementation of a semi-smooth Newton method for parabolic PDE-constraint optimization

Alexander Reinhold

10/04/2025, 09:10

PDE constraint optimization problems arise in a wide field of application and therefore the numerical analysis of these problems is a highly relevant research topic. In this talk, we consider a time-dependent optimization problem with a tracking type objective function and standard regularization. The equality constraint is a parabolic linear time-dependent PDE. We also consider additional box...

468. Automatic code generation for efficient matrix-free non-linear solvers with application to solid mechanics

Michał Wichrowski

10/04/2025, 09:30

We investigate the applicability of automatically generated code using AceGen to compute local quadrature point data in finite-strain hyperelasticity. We compare the matrix-free implementation of hand-written and AceGen-generated codes of compressible neo-Hookean models. To make the comparison more insightful, a traditional sparse matrix implementation is also included. Two strategies are...

469. IFDIFF - A Matlab Toolkit for ODEs with Filippov-type and State˗Dependent Switches

Andreas Sommer

10/04/2025, 09:50

We present the toolkit IFDIFF [1] for integration and sensitivity generation in parameterized implicitly (state-dependent) switched ODEs whose right-hand side is given as Matlab code containing non-differentiable operators (max, abs, etc.) and conditionals (if).

Naive implementations using IF-THEN-ELSE branching give unreliable simulation results without warning, as switching events are...

470. Spectral gaps for Laplacians of symplectic groups

Piotr Mizerka

10/04/2025, 10:10

During the last fifteen years, computer-assisted proofs have lead to the proofs of property (T) for several classes of groups. This property is in turn related to expanders, that is infinite families of sparse graphs with growing number of vertices and good connectivity properties. The quality of connectivity properties can be further estimated by means of Kazhdan constants. The common...

471. Higher-Order Projection Methods for Variable Viscosity Fluids

Richard Schussnig

10/04/2025, 14:00

Non-constant viscosity plays a crucial role in numerous incompressible flow problems of interest in science and engineering, with prime examples being polymer or blood flow. In such applications, the fluid’s viscosity depends on the local shear rate, where generalized Newtonian fluid models are considered an acceptable middle-ground between complexity and model capability. Standard...

472. Transient numerical investigation of fluid flow with the Fast Boundary-Domain Integral Method

Jan Tibaut

10/04/2025, 14:20

The development of new numerical methods for fluid flow simulations is challenging but such tools may help to understand flow problems better. Here, the Boundary-Domain Integral Method is applied to simulate laminar fluid flow governed by a dimensionless transient velocity-vorticity formulation of the Navier-Stokes equation. The Reynolds number is chosen in all examples small enough to ensure...

473. Smoothed aggregation algebraic multigrid for problems with heterogeneous and anisotropic material behavior

Max Firmbach

10/04/2025, 14:40

CANCELLED

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Many modern applications in engineering are faced to deal with heterogeneous and often anisotropic material behavior, relevant for thermal diffusion, groundwater flow or electrostatics. The numerical solution of these types of problems is challenging, as applying the finite element method results in badly scaled and ill-conditioned linear systems to be solved. To...

474. A Hybrid Ice Model

Saskia Kahl

10/04/2025, 15:00

The continuum viscous–plastic sea-ice model is widely used in climate models for simulating large-scale sea-ice dynamics, usually on grids of several kilometers (10 km). Recently, there is an increasing interest in modelling small-scale processes that have the potential to impact large-scale dynamics such as sea-ice–iceberg interactions. The influence of small-scale icebergs on sea-ice...

475. Matrix-free inexact preconditioning techniques for discretizations on structured grids

Michał Mika

10/04/2025, 15:20

We propose a matrix-free inexact preconditioned solution strategy for elliptic partial differential equations discretized by the Galerkin method on structured grids. We base our preconditioner on an approximation of the discrete linear operator by a sum of Kronecker product matrices. The action of the inverse of the approximation on a vector of coefficients is approximated by an inner...

790. NURBS fitting method for smoothed surface approximation in polymer additive manufacturing

Frederic Timmann

10/04/2025, 15:40

CANCELLED
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A key challenge in hybrid lightweight design is the joining of dissimilar materials such as metal and plastic. Environmentally and resource-orientated solutions are form-fit connections, as there is no need for additional adhesives. A current approach is the use of aluminium foam structures established in lightweight design to serve as undercuts that can be used for bonding...

477. Meshless Numerical Approach to Forced Convection Problems with Optimized Port Configuration

Chiung-Lin Chu, Chia-Ming Fan

10/04/2025, 16:30

This study presents an optimization model for forced convection problems, aiming to determine the optimal location and size of inlet and outlet ports in a cavity flow field. The proposed approach integrates the localized meshless method, the generalized finite difference method (GFDM) for spatial discretization, the projection method for stable and accurate simulation, and particle swarm...

478. Method of Fundamental Solutions with Domain-Decomposition Method and the Particle Swarm Optimization for Solving the Degenerate Boundary Problems

Tan Phat Lam

10/04/2025, 16:50

In this study, the Method of Fundamental Solutions (MFS) and the Domain-Decomposition Method (DDM) are integrated with Particle Swarm Optimization (PSO) to develop an efficient and robust framework for solving degenerate boundary problems. The MFS, inherently free from mesh generation and numerical quadrature, is recognized as a promising meshless method. Its implementation requires only field...

479. Numerical solutions of boundary detection problems by using the method of fundamental solution and the particle swarm optimization

Chia-Ming Fan

10/04/2025, 17:10

This study proposes combining the method of fundamental solutions (MFS) and particle swarm optimization (PSO) to accurately and stably analyze boundary detection problems. The boundary detection problems, considered in this study, are governed by the two-dimensional Laplace equation. In the boundary detection problems, the spatial position for part of the boundary portion is unknown, so it is...

480. Optimization of the exhaust unit geometry to minimize Ex-zone dimensions

Nils Kaufhold

10/04/2025, 17:30

When storing hydrogen in pressure vessels, there is a possibility that the stored hydrogen will be released into the atmosphere via exhaust units if the pressure rises above a maximum value. If the released hydrogen mixes with air, a potentially explosive atmosphere (Ex-zone) can result. This contribution examines the minimization of Ex-zone dimensions above vertical exhaust units on hydrogen...