A Monte Carlo method for solving unsteady adjoint equations

Authors:
Qiqi Wang;David Gleich;Amin Saberi;Nasrollah Etemadi;Parviz Moin
Affiliations:
Institute of Computational and Mathematical Engineering, Stanford University, Stanford, CA 94305, USA;Institute of Computational and Mathematical Engineering, Stanford University, Stanford, CA 94305, USA;Institute of Computational and Mathematical Engineering, Stanford University, Stanford, CA 94305, USA;Center for Turbulence Research, Stanford University, Stanford, CA 94305, USA;Center for Turbulence Research, Stanford University, Stanford, CA 94305, USA
Venue:
Journal of Computational Physics
Year:
2008

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Abstract

Traditionally, solving the adjoint equation for unsteady problems involves solving a large, structured linear system. This paper presents a variation on this technique and uses a Monte Carlo linear solver. The Monte Carlo solver yields a forward-time algorithm for solving unsteady adjoint equations. When applied to computing the adjoint associated with Burgers' equation, the Monte Carlo approach is faster for a large class of problems while preserving sufficient accuracy.