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|a Eftang, Jens L.
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|a Massachusetts Institute of Technology. Department of Mechanical Engineering
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|a Patera, Anthony T.
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|a Patera, Anthony T.
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|a Patera, Anthony T.
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|a Ronquist, Einar M.
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|a An "hp" Certified Reduced Basis Method for Parametrized Elliptic Partial Differential Equations
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|b Society for Industrial and Applied Mathematics,
|c 2010-09-03T20:43:14Z.
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|z Get fulltext
|u http://hdl.handle.net/1721.1/58468
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|a We present a new "hp" parameter multi-domain certified reduced basis 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.
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|a Norges teknisk-naturvitenskapelige universitet
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|a United States. Air Force Office of Scientific Research (Grant number FA 9550-07-1-0425 and OSD/AFOSR Grant number FA 9550-09-1-0613)
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|a Article
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|t SIAM Journal on Scientific Computing
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