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We describe a parallel solver for the discretized weakly singular space-time boundary integral equation of the spatially two-dimensional heat equation. The global space-time nature of the system matrices leads to improved parallel…

Numerical Analysis · Mathematics 2021-02-23 Stefan Dohr , Michal Merta , Günther Of , Olaf Steinbach , Jan Zapletal

Numerical solution of equations governing time domain simulations in computational electromagnetics, is usually based on grid methods in space and on explicit schemes for the time evolution. A predefined grid in the problem domain and a…

Numerical Analysis · Mathematics 2013-04-29 Guido Ala , Elisa Francomano

We present the first quantum-hardware implementation of a Hamiltonian simulation algorithm that produces signed vector-field solutions to the time-domain Maxwells equations using a Schrodingerisation-based approach. The electromagnetic…

Quantum Physics · Physics 2026-05-05 Gautam Sharma , Apurva Tiwari , Niladri Gomes , Jezer Jojo , J. Eric Bracken , Jay Pathak

We present GRaM-X (General Relativistic accelerated Magnetohydrodynamics on AMReX), a new GPU-accelerated dynamical-spacetime general relativistic magnetohydrodynamics (GRMHD) code which extends the GRMHD capability of Einstein Toolkit to…

Instrumentation and Methods for Astrophysics · Physics 2025-12-23 Swapnil Shankar , Philipp Mösta , Steven R. Brandt , Roland Haas , Erik Schnetter , Yannick de Graaf

In this work, we present a comprehensive numerical framework that couples numerical solutions of Maxwell's equations using the Finite-Difference Time-Domain (FDTD) approach, Molecular Dynamics (MD), and the Two-Temperature Model (TTM) to…

Materials Science · Physics 2026-01-29 Othmane Benhayoun , Martin E. Garcia

This paper proposes an efficient parallelised computation of field/circuit coupled systems co-simulated with the Waveform Relaxation (WR) technique. The main idea of the introduced approach lies in application of the parallel-in-time method…

Computational Physics · Physics 2020-03-17 Idoia Cortes Garcia , Iryna Kulchytska-Ruchka , Sebastian Schöps

We propose in this paper the Wavelet-based Edge Multiscale Parareal (WEMP) Algorithm to efficiently solve parabolic equations with heterogeneous coefficients. This algorithm combines the advantages of multiscale methods that can deal with…

Numerical Analysis · Mathematics 2021-08-18 Guanglian Li , Jiuhua Hu

This paper addresses the problem of parallelizing computations to study non-linear dynamics in large networks of non-locally coupled oscillators using heterogeneous computing resources. The proposed approach can be applied to a variety of…

Chaotic Dynamics · Physics 2025-07-04 Oleksandr Sudakov , Volodymyr Maistrenko

We introduce a micro-macro parareal algorithm for the time-parallel integration of multiscale-in-time systems. The algorithm first computes a cheap, but inaccurate, solution using a coarse propagator (simulating an approximate slow…

Numerical Analysis · Mathematics 2013-02-11 Frederic Legoll , Tony Lelievre , Giovanni Samaey

A novel electromagnetic particle-in-cell algorithm has been developed for fully kinetic plasma simulations on unstructured (irregular) meshes in complex body-of-revolution geometries. The algorithm, implemented in the BORPIC++ code,…

Numerical Analysis · Mathematics 2024-05-16 Dong-Yeop Na , Fernando L. Teixeira , Yuri A. Omelchenko

This paper presents the research work on multicore microcontrollers using parallel, and time critical programming for the embedded systems. Due to the high complexity and limitations, it is very hard to work on the application development…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-04-13 Prerna Saini , Ankit Bansal , Abhishek Sharma

Motivated by recent models of current driven magnetization dynamics, we examine the coupling of the Landau-Lifshitz-Gilbert equation and classical electron transport governed by the Vlasov-Maxwell system. The interaction is based on…

Analysis of PDEs · Mathematics 2021-12-01 Tvrtko Dorešić , Christof Melcher

We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…

Numerical Analysis · Mathematics 2025-12-16 Leonardo A. Poveda , Shubin Fu , Guanglian Li , Eric Chung

In this paper, we propose a numerical method for the solution of time-dependent flow problems in mixed form. Such problems can be efficiently approximated on hierarchical grids, obtained from an unstructured coarse triangulation by using a…

Numerical Analysis · Mathematics 2017-02-10 Andrés Arrarás , Laura Portero

We propose a parallel algorithm for the numerical solution of a class of second order semi-linear equations coming from stochastic optimal control problems, by means of a dynamic domain decomposition technique. The new method is an…

Numerical Analysis · Mathematics 2016-02-11 Simone Cacace , Maurizio Falcone

This work introduces an approach to compute periodic phase diagram of micromagnetic systems by solving a periodic linearized Landau-Lifshitz-Gilbert (LLG) equation using an eigenvalue solver with the Finite Element Method formalism. The…

Materials Science · Physics 2024-11-13 Fangzhou Ai , Zhuonan Lin , Jiawei Duan , Vitaliy Lomakin

We present a novel parallel implementation for large-scale three-dimensional electromagnetic inversion based on a Gauss-Newton framework combined with a rational near-best approximation of the matrix exponential for transient simulations.…

Numerical Analysis · Mathematics 2026-05-20 Ralph-Uwe Börner , Stefan Güttel , Thomas Günther

An adpative integration technique for time advancement of particle motion in the context of coupled computational fluid dynamics (CFD) - discrete element method (DEM) simulations is presented in this work. CFD-DEM models provide an accurate…

Computational Physics · Physics 2018-02-28 Hariswaran Sitaraman , Ray Grout

Efficient modeling of dispersive materials via time-domain simulations of the Maxwell equations relies on the technique of auxiliary differential equations. In this approach, a material's frequency-dependent permittivity is represented via…

This work introduces a semi-analytical frequency-domain framework for the analysis of two-dimensional, time-modulated (2+1)-D metasurfaces controlled by PIN diodes. The formulation focuses on the unit-cell level, modeled as a waveguide…