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We present an efficient integral equation approach to solve the heat equation, $u_t (\x) - \Delta u(\x) = F(\x,t)$, in a two-dimensional, multiply connected domain, and with Dirichlet boundary conditions. Instead of using integral equations…

Numerical Analysis · Mathematics 2010-08-02 Mary-Catherine Kropinski , Bryan Quaife

A new fast multipole formulation for solving elliptic difference equations on unbounded domains and its parallel implementation are presented. These difference equations can arise directly in the description of physical systems, e.g.…

Computational Physics · Physics 2016-04-08 Sebastian Liska , Tim Colonius

We present a family of integral equation-based solvers for the linear or semilinear heat equation in complicated moving (or stationary) geometries. This approach has significant advantages over more standard finite element or finite…

Numerical Analysis · Mathematics 2022-12-06 Jun Wang , Leslie Greengard , Shidong Jiang , Shravan Veerapaneni

This paper is devoted to the problem of time parallelization of assimilation methods applying on unbounded time domain. In this way, we present a general procedure to couple the Luenberger observer with time parallelization algorithm. Our…

Optimization and Control · Mathematics 2022-12-06 Sebastián Riffo , Félix Kwok , Julien Salomon

Understanding the complex behavior of molecular systems is fundamental to fields such as physics, materials science, and biology. Molecular dynamics (MD) simulations are crucial tools for studying atomic-level dynamics. This work focuses on…

Computational Engineering, Finance, and Science · Computer Science 2025-07-16 David Martin , Samuel James Newcome , Markus Mühlhäußer , Manish Kumar Mishra , Fabio Alexander Gratl , Hans-Joachim Bungartz

In this paper, three efficient ensemble algorithms are proposed for fast-solving the random fluid-fluid interaction model. Such a model can be simplified as coupling two heat equations with random diffusion coefficients and a friction…

Numerical Analysis · Mathematics 2023-01-24 Yizhong Sun , Jiangshan Wang , Haibiao Zheng

This paper introduces an ultra-weak space-time DPG method for the heat equation. We prove well-posedness of the variational formulation with broken test functions and verify quasi-optimality of a practical DPG scheme. Numerical experiments…

Numerical Analysis · Mathematics 2021-06-18 Lars Diening , Johannes Storn

The aim of the paper is to introduce general techniques in order to optimize the parallel execution time of sorting on a distributed architectures with processors of various speeds. Such an application requires a partitioning step. For…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-08-16 Christophe Cérin , Jean-Christophe Dubacq , Jean-Louis Roch , the SafeScale Collaboration

This paper presents a novel space-time topology optimisation framework for time-dependent thermal conduction problems, aiming to significantly reduce the time-to-solution. By treating time as an additional spatial dimension, we discretise…

Computational Engineering, Finance, and Science · Computer Science 2025-08-14 Joe Alexandersen , Magnus Appel

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

In this paper, we employ a space-time finite element method to discretize the parabolic initial-boundary value problem and extend its error analysis with refined estimates on unstructured space-time meshes. We establish higher-order…

Numerical Analysis · Mathematics 2025-03-13 Thi Thanh Mai Ta , Quang Huy Nguyen , Phi Hung Pham

In theory, diffusion curves promise complex color gradations for infinite-resolution vector graphics. In practice, existing realizations suffer from poor scaling, discretization artifacts, or insufficient support for rich boundary…

Numerical Analysis · Mathematics 2023-11-27 Seungbae Bang , Kirill Serkh , Oded Stein , Alec Jacobson

Parametric linear programming is a central operation for polyhedral computations, as well as in certain control applications.Here we propose a task-based scheme for parallelizing it, with quasi-linear speedup over large problems.This type…

Computational Geometry · Computer Science 2020-10-01 Camille Coti , David Monniaux , Hang Yu

We present a fast adaptive method for the evaluation of heat potentials, which plays a key role in the integral equation approach for the solution of the heat equation, especially in a non-stationary domain. The algorithm utilizes a…

Numerical Analysis · Mathematics 2024-12-06 Chengyue Song , Jun Wang

Rapid processes of heat transfer are not described by the standard heat conduction equation. To take into account a finite velocity of heat transfer, we use the hyperbolic model of heat conduction, which is connected with the relaxation of…

Numerical Analysis · Computer Science 2010-10-13 Petr N. Vabishchevich

We present a new approach to three-dimensional electromagnetic scattering problems via fast isogeometric boundary element methods. Starting with an investigation of the theoretical setting around the electric field integral equation within…

Numerical Analysis · Mathematics 2019-06-28 Jürgen Dölz , Stefan Kurz , Sebastian Schöps , Felix Wolf

In this paper, we present a method that enables to solve in parallel the Euler-Lagrange system associated with the optimal control of a parabolic equation. Our approach is based on an iterative update of a sequence of intermediate targets…

Optimization and Control · Mathematics 2011-10-19 Yvon Maday , Julien Salomon , Kamel Riahi

We discuss the efficiency of parallelization on graphical processing units (GPUs) for the simulation of the one dimensional Potts model with long range interactions via parallel tempering. We investigate the behaviour of some thermodynamic…

Statistical Mechanics · Physics 2015-06-17 A. Boer

In this contribution the usage of the Parareal method is proposed for the time-parallel solution of the eddy current problem. The method is adapted to the particular challenges of the problem that are related to the differential algebraic…

Computational Engineering, Finance, and Science · Computer Science 2018-02-08 Sebastian Schöps , Innocent Niyonzima , Markus Clemens

We present a space-time multiscale method for a parabolic model problem with an underlying coefficient that may be highly oscillatory with respect to both the spatial and the temporal variables. The method is based on the framework of the…

Numerical Analysis · Mathematics 2021-12-13 Per Ljung , Roland Maier , Axel Målqvist