An adaptive stochastic Galerkin method for random elliptic operators
An adaptive stochastic Galerkin method for random elliptic operators
复制标题
随机椭圆算子的自适应随机Galerkin方法
DOI：
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发表时间：
2013
影响因子：
2
通讯作者：
C. J. Gittelson
中科院分区：
文献类型：
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作者：
C. J. Gittelson
。利用自适应小波方法，导出了随机椭圆边值问题的自适应求解器。用随机参数的多项式代替小波，得到了随机解的参数依赖性的模求解器，它与空间域上的任意离散化相结合。除了选择主动多项式模式外，该求解器还可以自适应地为每个系数构建单独的空间离散化。在这种一般情况下，我们展示了求解器的收敛性，以及均方误差的可计算界，以及单个空间离散情况下的最优性。数值计算证明了求解器的收敛性，并将其与稀疏张量积构造进行了比较。
. We derive an adaptive solver for random elliptic boundary value problems, using techniques from adaptive wavelet methods. Substituting wave- lets by polynomials of the random parameters leads to a modular solver for the parameter dependence of the random solution, which combines with any dis- cretization on the spatial domain. In addition to selecting active polynomial modes, this solver can adaptively construct a separate spatial discretization for each of their coefficients. We show convergence of the solver in this general setting, along with a computable bound for the mean square error, and an optimality property in the case of a single spatial discretization. Numerical computations demonstrate convergence of the solver and compare it to a sparse tensor product construction.