Adaptive Numerical Solutions of Stochastic Differential Equations
نویسنده
چکیده
In this paper we present an adaptive multi-element generalized polynomial chaos (ME-gPC) method, which can achieve hp-convergence in random space. ME-gPC is based on the decomposition of random space and generalized polynomial chaos (gPC). Using proper numerical schemes to maintain the local orthogonality on-the-fly, we perform gPC locally and adaptively. The key idea is to combine the polynomial chaos method of h version and p version. The adaptive ME-gPC shows good performance in dealing with problems related to long-term integration, large perturbation and discontinuities. Benchmarks and applications of ME-gPC are presented.
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