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We propose and investigate new robust preconditioners for space-time Isogeometric Analysis of parabolic evolution problems. These preconditioners are based on a time parallel multigrid method. We consider a decomposition of the space-time…

Numerical Analysis · Mathematics 2018-02-27 Christoph Hofer , Ulrich Langer , Martin Neumüller

We consider the numerical solution of large scale time-harmonic Maxwell equations. To this day, this problem remains difficult, in particular because the equations are neither Hermitian nor semi-definite. Our approach is to compare…

Numerical Analysis · Mathematics 2025-07-18 Elise Fressart , Sébastien Dubois , Loïc Gouarin , Marc Massot , Michel Nowak , Nicole Spillane

In this paper we propose a multiscale method for the acoustic wave equation in highly oscillatory media. We use a higher-order extension of the localized orthogonal decomposition method combined with a higher-order time stepping scheme and…

Numerical Analysis · Mathematics 2024-07-23 Felix Krumbiegel , Roland Maier

We derive a new parallel-in-time approach for solving large-scale optimization problems constrained by time-dependent partial differential equations arising from fluid dynamics. The solver involves the use of a block circulant approximation…

Numerical Analysis · Mathematics 2024-05-30 Bernhard Heinzelreiter , John W. Pearson

The high cost of sequential time integration is one major constraint that limits the speedup of a time-parallel algorithm like the Parareal algorithm due to the difficulty of coarsening time steps in a stiff numerical problem. To address…

Computational Physics · Physics 2025-03-06 Weifan Liu

In view of the existing limitations of sequential computing, parallelization has emerged as an alternative in order to improve the speedup of numerical simulations. In the framework of evolutionary problems, space-time parallel methods…

Numerical Analysis · Mathematics 2025-02-13 Andrés Arrarás , Francisco J. Gaspar , Iñigo Jimenez-Ciga , Laura Portero

This work presents a new Krylov-subspace-recycling method for efficiently solving sequences of linear systems of equations characterized by varying right-hand sides and symmetric-positive-definite matrices. As opposed to typical truncation…

Numerical Analysis · Mathematics 2016-01-22 Kevin Carlberg , Virginia Forstall , Ray Tuminaro

Among optimal hierarchical algorithms for the computational solution of elliptic problems, the Fast Multipole Method (FMM) stands out for its adaptability to emerging architectures, having high arithmetic intensity, tunable accuracy, and…

Numerical Analysis · Computer Science 2016-01-20 Huda Ibeid , Rio Yokota , Jennifer Pestana , David Keyes

This note proposes an efficient preconditioner for solving linear and semi-linear parabolic equations. With the Crank-Nicholson time stepping method, the algebraic system of equations at each time step is solved with the conjugate gradient…

Numerical Analysis · Mathematics 2021-05-11 Jordi Feliu-Fabà , Lexing Ying

Due to the wide separation of time scales in geophysical fluid dynamics, semi-implicit time integrators are commonly used in operational atmospheric forecast models. They guarantee the stable treatment of fast (acoustic and gravity) waves,…

Computational Physics · Physics 2020-12-30 Christopher Maynard , Thomas Melvin , Eike Hermann Müller

A delay Lyapunov matrix corresponding to an exponentially stable system of linear time-invariant delay differential equations can be characterized as the solution of a boundary value problem involving a matrix valued delay differential…

Numerical Analysis · Mathematics 2018-08-28 Wim Michiels , Bin Zhou

In this paper we solve the Helmholtz equation with multigrid preconditioned Krylov subspace methods. The class of Shifted Laplacian preconditioners are known to significantly speed-up Krylov convergence. However, these preconditioners have…

Analysis of PDEs · Mathematics 2013-09-06 Siegfried Cools , Wim Vanroose

The goal of this work is to present a fast and viable approach for the numerical solution of the high-contrast state problems arising in topology optimization. The optimization process is iterative, and the gradients are obtained by an…

Numerical Analysis · Mathematics 2020-06-25 Miguel Zambrano , Sintya Serrano , Boyan S. Lazarov , Juan Galvis

We present a Calder\'on preconditioning scheme for the symmetric formulation of the forward electroencephalographic (EEG) problem that cures both the dense discretization and the high-contrast breakdown. Unlike existing Calder\'on schemes…

Numerical Analysis · Mathematics 2023-08-16 Viviana Giunzioni , John E. Ortiz G. , Adrien Merlini , Simon B. Adrian , Francesco P. Andriulli

We present and analyze a discontinuous Galerkin method for the numerical modelling of the non-linear fully-coupled thermo-poroelastic problem. For the spatial discretization, we design a high-order discontinuous Galerkin method on polygonal…

Numerical Analysis · Mathematics 2022-05-27 Paola F. Antonietti , Stefano Bonetti , Michele Botti

This paper describes a massively parallel algebraic multigrid method based on non-smoothed aggregation. It is especially suited for solving heterogeneous elliptic problems as it uses a greedy heuristic algorithm for the aggregation that…

Numerical Analysis · Mathematics 2013-10-01 Markus Blatt , Olaf Ippisch , Peter Bastian

We develop a space-time mortar mixed finite element method for parabolic problems. The domain is decomposed into a union of subdomains discretized with non-matching spatial grids and asynchronous time steps. The method is based on a…

Numerical Analysis · Mathematics 2021-10-06 Manu Jayadharan , Michel Kern , Martin Vohralík , Ivan Yotov

This paper presents algorithms for parallelization of inference in hidden Markov models (HMMs). In particular, we propose parallel backward-forward type of filtering and smoothing algorithm as well as parallel Viterbi-type…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-09-07 Sakira Hassan , Simo Särkkä , Ángel F. García-Fernández

In this paper, we suggest a new heterogeneous multiscale method (HMM) for the time-harmonic Maxwell equations in locally periodic media. The method is constructed by using a divergence-regularization in one of the cell problems. This allows…

Numerical Analysis · Mathematics 2015-09-15 Patrick Henning , Mario Ohlberger , Barbara Verfürth

We present a compatible space-time hybridizable/embedded discontinuous Galerkin discretization for nonlinear free-surface waves. We pose this problem in a two-fluid (liquid and gas) domain and use a time-dependent level-set function to…

Numerical Analysis · Mathematics 2023-07-10 Giselle Sosa Jones , Sander Rhebergen