What is it about?
There are intrusive and non-intrusive methods to quantify uncertainty or to solve a stochastic PDE. Intrusive *means* that we need to modify the existing deterministic solver, and non-intrusive - do not need (gPCE, stochastic collocation, sparse grids ). It this paper we show that such division in intrusive and non-intrusive methods is not so accurate. For example, many of us are thinking that the stochastic Galerkin is an intrusive method. Indeed, it may require to compute the KLE and gPCE expansions incorporate both into the existing Galerkin procedure, recompute the bilinear form, rewrite the the iterative solver etc. We show that it is not necessary. We show that the stochastic Galerkin method can be reformulated in a non-intrusive way, so that no code-changes are needed. At the end we compare non-intrusive stochastic Galerkin with the stochastic collocation. Everything what is needed is the access to the residual.
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Why is it important?
We preserve all advantages of the intrusive method (e.g., faster convergence, reusing of nice properties of the operator) and eliminate disadvantages (modification of the existing and well-tested deterministic code).
Perspectives
It allows to re-use existing, well-tuned, well-tested, black-box, probably commercial, code in the stochastic framework in a non-intrusive way. The need to change the existing code prevented many engineering groups from solving/investigating uncertainty quantification issues. Now this barrier is broken.
Dr. Alexander Litvinenko
Rheinisch Westfalische Technische Hochschule Aachen
Read the Original
This page is a summary of: To Be or Not to Be Intrusive? The Solution of Parametric and Stochastic Equations---the “Plain Vanilla” Galerkin Case, SIAM Journal on Scientific Computing, January 2014, Society for Industrial & Applied Mathematics (SIAM),
DOI: 10.1137/130942802.
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