%0 Journal Article
%4 sid.inpe.br/mtc-m21c/2019/02.14.12.45
%2 sid.inpe.br/mtc-m21c/2019/02.14.12.45.33
%@doi 10.1016/j.jcp.2018.10.052
%@issn 0021-9991
%T Local time-stepping for adaptive multiresolution using natural extension of Runge–Kutta methods
%D 2019
%8 Apr.
%9 journal article
%A Lopes, Müller Moreira,
%A Domingues, Margarete Oliveira,
%A Schneider, Kai,
%A Mendes, Odim,
%@affiliation Instituto Nacional de Pesquisas Espaciais (INPE)
%@affiliation Instituto Nacional de Pesquisas Espaciais (INPE)
%@affiliation Institut de Mathématiques de Marseille (I2M), Aix-Marseille Université
%@affiliation Instituto Nacional de Pesquisas Espaciais (INPE)
%@electronicmailaddress muller.lopes@inpe.br
%@electronicmailaddress margarete.domingues@inpe.br
%@electronicmailaddress kai.schneider@univ-amu.fr
%@electronicmailaddress odim.mendes@inpe.br
%B Journal of Computational Physics
%V 382
%P 291-318
%K Multiresolution analysis, Finite volume, Local time-stepping, Runge–Kutta.
%X A spacetime fully adaptive multiresolution method for evolutionary non-linear partial differential equations is presented introducing an improved local time-stepping method. The space discretisation is based on classical finite volumes, endowed with cell average multiresolution analysis for triggering the dynamical grid adaptation. The explicit time scheme features a natural extension of RungeKutta methods which allow local time-stepping while guaranteeing accuracy. The use of a compact RungeKutta formulation permits further memory reduction. The precision and computational efficiency of the scheme regarding CPU time and memory compression are assessed for problems in one, two and three space dimensions. As application Burgers equation, reactiondiffusion equations and the compressible Euler equations are considered. The numerical results illustrate the efficiency and superiority of the proposed local time-stepping method with respect to the reference computations.
%@language en
%3 lopes_local.pdf