An '$hp$' Certified Reduced Basis Method for Parametrized Elliptic Partial Differential Equations

Autor:	Jens L. Eftang, Anthony T. Patera, Einar M. Rønquist
Rok vydání:	2010
Předmět:	Computational Mathematics Elliptic curve Multigrid method Partial differential equation Elliptic partial differential equation Applied Mathematics Numerical analysis Applied mathematics Initial value problem Domain decomposition methods Boundary value problem Mathematics
Zdroj:	SIAM Journal on Scientific Computing. 32:3170-3200
ISSN:	1095-7197 1064-8275
DOI:	10.1137/090780122
Popis:	We present a new “$hp$” parameter multidomain certified reduced basis (RB) method for rapid and reliable online evaluation of functional outputs associated with parametrized elliptic partial differential equations. We propose, and provide theoretical justification for, a new procedure for adaptive partition (“$h$”-refinement) of the parameter domain into smaller parameter subdomains: we pursue a hierarchical splitting of the parameter (sub)domains based on proximity to judiciously chosen parameter anchor points within each subdomain. Subsequently, we construct individual standard RB approximation spaces (“$p$”-refinement) over each subdomain. Greedy parameter sampling procedures and a posteriori error estimation play important roles in both the “$h$”-type and “$p$”-type stages of the new algorithm. We present illustrative numerical results for a convection-diffusion problem: the new “$hp$”-approach is considerably faster (respectively, more costly) than the standard “$p$”-type reduced basis method in the online (respectively, offline) stage.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::fb140ca9cf9b4893484228276281fa7c https://doi.org/10.1137/090780122 Zobrazit plný text záznamu Plný text ve formátu PDF