The termsurrogate modeling'in computational science and engineering refers to the
development of computationally efficient approximations for expensive simulations, such as …

We provide a concise review of the exponentially convergent multiscale finite element
method (ExpMsFEM) for efficient model reduction of PDEs in heterogeneous media without …

In this paper, a generalized finite element (FE) method with optimal local approximation
spaces for solving high-frequency heterogeneous Helmholtz problems is systematically …

We consider approximating the solution of the Helmholtz exterior Dirichlet problem for a
nontrapping obstacle, with boundary data coming from plane-wave incidence, by the …

We propose a novel variant of the Localized Orthogonal Decomposition (LOD) method for
time-harmonic scattering problems of Helmholtz type with high wavenumber. On a coarse …

This work presents an abstract framework for the design, implementation, and analysis of the
multiscale spectral generalized finite element method (MS-GFEM), a particular numerical …

This paper develops a multiscale solver for the problem of two languages competing in a
heterogeneous medium. The mathematical model contains terms for language group …

In this paper, a generalized finite element method (GFEM) with optimal local approximation
spaces for solving high-frequency heterogeneous Helmholtz problems is systematically …

This paper proposes a two-level restricted additive Schwarz (RAS) method for multiscale
PDEs, built on top of a multiscale spectral generalized finite element method (MS-GFEM) …

Homogenisation empowers the efficient macroscale system level prediction of physical
problems with intricate microscale structures. Here we develop an innovative powerful …