Novel results for the anisotropic sparse grid quadrature
For researchers in numerical analysis and scientific computing, this work offers improved theoretical guarantees for anisotropic sparse grid quadrature, though it is an incremental advance over existing methods.
The paper provides dimension-independent error-cost estimates for anisotropic sparse grid quadrature for analytic functions, and improves the cardinality estimate of the anisotropic index set. Numerical examples confirm the method's convergence.
This article is dedicated to the anisotropic sparse grid quadrature for functions which are analytically extendable into an anisotropic tensor product domain. Taking into account this anisotropy, we end up with a dimension independent error versus cost estimate of the proposed quadrature. In addition, we provide a novel and improved estimate for the cardinality of the underlying anisotropic index set. To validate the theoretical findings, we present several examples ranging from simple quadrature problems to diffusion problems on random domains. These examples demonstrate the remarkable convergence behaviour of the anisotropic sparse grid quadrature in applications.