A Monte Carlo Method for solving linear and integral equations based on simulating one realization of an ergodic Markov chain is proposed. The efficiency of the proposed method is discussed. ' The Markov chain need not be homogeneous; we are considering the homogeneous case for simplicity only.
A Monte Carlo method for solving unsteady adjoint equations
โ Scribed by Qiqi Wang; David Gleich; Amin Saberi; Nasrollah Etemadi; Parviz Moin
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 548 KB
- Volume
- 227
- Category
- Article
- ISSN
- 0021-9991
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โฆ Synopsis
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.
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