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Classical multi-scale methods involving two spatial scales face significant challenges when simulating heterogeneous structures with complicated three-scale spatial configurations. This study proposes an innovative higher-order three-scale…

Numerical Analysis · Mathematics 2025-12-11 Hao Dong , Yanqi Wang , Jiale Linghu , Qiang Ma

Dispersion-free ultra-high order FFT-based Maxwell solvers have recently proven to be paramount to a large range of applications, including the high-fidelity modeling of high-intensity laser-matter interactions with Particle-In-Cell (PIC)…

Computational Physics · Physics 2019-10-02 Haithem Kallala , Jean-Luc Vay , Henri Vincenti

Model-based iterative reconstruction plays a key role in solving inverse problems. However, the associated minimization problems are generally large-scale, nonsmooth, and sometimes even nonconvex, which present challenges in designing…

Image and Video Processing · Electrical Eng. & Systems 2025-10-21 Tao Hong , Zhaoyi Xu , Jason Hu , Jeffrey A. Fessler

In-memory computing (IMC) has been shown to be a promising approach for solving binary optimization problems while significantly reducing energy and latency. Building on the advantages of parallel computation, we propose an IMC-compatible…

We consider piecewise polynomial discontinuous Galerkin discretizations of boundary integral reformulations of the heat equation. The resulting linear systems are dense and block-lower triangular and hence can be solved by block forward…

Numerical Analysis · Mathematics 2024-08-09 Sivaram Ambikasaran , Ritesh Khan , Johannes Tausch , Sihao Wang

We present a novel solver technique for the anisotropic heat flux equation, aimed at the high level of anisotropy seen in magnetic confinement fusion plasmas. Such problems pose two major challenges: (i) discretization accuracy and (ii)…

Numerical Analysis · Mathematics 2024-03-15 Golo A. Wimmer , Ben S. Southworth , Thomas J. Gregory , Xian-Zhu Tang

We address in this thesis the current need to design new parallel algorithms and tools that ease the development of geodynamic modelling applications that are suited for today's and tomorrow's hardware. We present (1) the MATLAB HPC…

Geophysics · Physics 2022-07-19 Samuel Omlin , Ludovic Räss , Benjamin Malvoisin , Yury Y. Podladchikov

The observed and expected continued growth in the number of nodes in large-scale parallel computers gives rise to two major challenges: global communication operations are becoming major bottlenecks due to their limited scalability, and the…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-02-03 Markus Levonyak , Christina Pacher , Wilfried N. Gansterer

We propose a multilevel approach for trace systems resulting from hybridized discontinuous Galerkin (HDG) methods. The key is to blend ideas from nested dissection, domain decomposition, and high-order characteristic of HDG discretizations.…

Numerical Analysis · Mathematics 2020-02-19 Sriramkrishnan Muralikrishnan , Tan Bui-Thanh , John N. Shadid

In this work, we design and analyze a novel, provably conditionally stable, weakly coupled partitioned scheme to solve the conjugate heat transfer (CHT) problem. We consider a model CHT problem consisting of linear advection-diffusion and…

Numerical Analysis · Mathematics 2026-02-23 Sarah Nataj , David C. Del Rey Fernández , David Brown , Rajeev Jaiman

We describe an implementation of compressible inviscid fluid solvers with block-structured adaptive mesh refinement on Graphics Processing Units using NVIDIA's CUDA. We show that a class of high resolution shock capturing schemes can be…

Cosmology and Nongalactic Astrophysics · Physics 2014-11-20 Peng Wang , Tom Abel , Ralf Kaehler

High-order implicit shock tracking (fitting) is a class of high-order numerical methods that use numerical optimization to simultaneously compute a high-order approximation to a conservation law solution and align elements of the…

Numerical Analysis · Mathematics 2024-06-28 Jakob Vandergrift , Matthew J. Zahr

We use high order finite difference methods to solve the wave equation in the second order form. The spatial discretization is performed by finite difference operators satisfying a summation-by-parts property. The focus of this work is on…

Numerical Analysis · Mathematics 2017-02-08 Siyang Wang , Kristoffer Virta , Gunilla Kreiss

In this article, we present a parallel discretization and solution method for parabolic problems with a higher number of space dimensions. It consists of a parallel-in-time approach using the multigrid reduction-in-time algorithm MGRIT with…

Numerical Analysis · Mathematics 2026-05-01 Michael Griebel , Marc Alexander Schweitzer , Lukas Troska

In this paper we present an optimized parallel implementation of a flexible MAP decoder for synchronization error correcting codes, supporting a very wide range of code sizes and channel conditions. On mid-range GPUs we demonstrate decoding…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-02-26 Johann A. Briffa

In this paper we propose two variants of the substructuring preconditioner for solving three-dimensional elliptic-type equations with strongly discontinuous coefficients. In the new preconditioners, we use the simplest coarse solver…

Numerical Analysis · Mathematics 2016-11-29 Qiya Hu , Shaoliang Hu

We present an efficient, robust and fully GPU-accelerated aggregation-based algebraic multigrid preconditioning technique for the solution of large sparse linear systems. These linear systems arise from the discretization of elliptic PDEs.…

Numerical Analysis · Mathematics 2014-03-10 Rajesh Gandham , Ken Esler , Yongpeng Zhang

The Helmholtz equation is related to seismic exploration, sonar, antennas, and medical imaging applications. It is one of the most challenging problems to solve in terms of accuracy and convergence due to the scalability issues of the…

Numerical Analysis · Mathematics 2024-01-12 Jinqiang Chen , Vandana Dwarka , Cornelis Vuik

We discuss vertex patch smoothers as overlapping domain decomposition methods for fourth order elliptic partial differential equations. We show that they are numerically very efficient and yield high convergence rates. Furthermore, we…

Numerical Analysis · Mathematics 2025-06-23 Julius Witte , Cu Cui , Francesca Bonizzoni , Guido Kanschat

This work aims to accelerate the convergence of proximal gradient methods used to solve regularized linear inverse problems. This is achieved by designing a polynomial-based preconditioner that targets the eigenvalue spectrum of the normal…