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An experimental comparison of a space-time multigrid method with PFASST for a reaction-diffusion problem

Benedusi, Pietro ; Minion, Michael L. ; Krause, Rolf

In: Computers and mathematics with applications, 2021, vol. 99, p. 162-170

We consider two parallel-in-time approaches applied to a (reaction) diffusion problem, possibly non-linear. In particular, we consider PFASST (Parallel Full Approximation Scheme in Space and Time) and space-time multigrid strategies. For both approaches, we start from an integral formulation of the continuous time dependent problem. Then, a collocation form for PFASST and a discontinuous ...

Multigrid methods for fractional diffusion equations

Trotti, Ken ; Krause, Rolf (Dir.) ; Donatelli, Marco (Codir.)

Thèse de doctorat : Università della Svizzera italiana, 2021 ; 2021INFO013.

Recent years have seen the rapid growth in interest towards fractional calculus. Fractional calculus plays an important role in modelling anomalous diffusion phenomena, however closed-form analytical solutions of such equations are rarely available, hence numerical estimates are needed. In this thesis we consider various fractional diffusion equations (FDEs), where different fractional ...

Heuristic strategies for the approximation of stability factors in quadratically nonlinear parametrized PDEs

Manzoni, Andrea ; Negri, Federico

In: Advances in Computational Mathematics, 2015, vol. 41, no. 5, p. 1255-1288

An adaptive space-time Newton-Galerkin approach for semilinear singularly perturbed parabolic evolution equations

Amrein, Mario ; Wihler, Thomas P.

In: IMA Journal of Numerical Analysis, 2017, vol. 37, no. 4, p. 2004-2019

A multidomain discretization of the Richards equation in layered soil

Berninger, Heiko ; Kornhuber, Ralf ; Sander, Oliver

In: Computational Geosciences, 2015, vol. 19, no. 1, p. 213-232

Center-stable manifold of the ground state in the energy space for the critical wave equation

Krieger, Joachim ; Nakanishi, Kenji ; Schlag, Wilhelm

In: Mathematische Annalen, 2015, vol. 361, no. 1-2, p. 1-50

Isogeometric rotation-free analysis of planar extensible-elastica for static and dynamic applications

Maurin, Florian ; Dedè, Luca ; Spadoni, Alessandro

In: Nonlinear Dynamics, 2015, vol. 81, no. 1-2, p. 77-96

On the numerical solution of some Eikonal equations: An elliptic solver approach

Caboussat, Alexandre ; Glowinski, Roland ; Pan, Tsorng-Whay

In: Chinese Annals of Mathematics, Series B, 2015, vol. 36, no. 5, p. 689-702

On multiscale methods in Petrov-Galerkin formulation

Elfverson, Daniel ; Ginting, Victor ; Henning, Patrick

In: Numerische Mathematik, 2015, vol. 131, no. 4, p. 643-682

Optimal A Priori Discretization Error Bounds for Geodesic Finite Elements

Grohs, Philipp ; Hardering, Hanne ; Sander, Oliver

In: Foundations of Computational Mathematics, 2015, vol. 15, no. 6, p. 1357-1411