AN "hp" CERTIFIED REDUCED BASIS METHOD FOR PARAMETRIZED ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS

作者：Eftang Jens L^*; Patera Anthony T; Ronquist Einar M

来源：SIAM Journal on Scientific Computing, 2010, 32(6): 3170-3200.

DOI：10.1137/090780122

• reduced basis
• a posteriori error estimation
• Greedy sampling
• h-type
• p-type
• hp convergence
• parameter domain decomposition

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.

• 出版日期2010