… The coarse grid method is used for solving the solid elastic … finite element discretizations as
fine grid methods for solving … a stabilized finite element discretization for solving the Navier–…

… multiscale model by directly embedding a full-field CP-spectral solver in an implicit finite
element … are employed in this work to test the new fully integrated multiscale model. Simple …

… The general multiscale finite element framework proposed in … solvers that use the coarse
spaces and iterate on the residual to converge to the fine-scale solution. These iterative solvers …

… Well-known numerical methods widely applied for problem solving in the mechanics of
discontinua are discrete element methods (DEM). The term DEM implies a large group of …

… complicated and large geological models. Based on the generalized multiscale finite-element
theory, we develop a novel continuous Galerkin method to solve the Helmholtz equation in …

… solver, the MsMFE method has a natural parallelism that can be exploited on multicore and
parallel computers. Finally, multiscale … assume the classical multiscale modeling approach in …

… novel multiscale model reduction technique for solving many … our unified approach for local
multiscale model reduction; (2) … applications to a variety of challenging multiscale problems. …

… In this work, we explore the idea of multiscale modeling with machine learning and employ
… the expensive solver. DeepONet is trained offline using data acquired from the fine solver for …

… Thus, we perform one linear finite element solve (including assembly, etc.) consisting of
28.9 million equations in ∼8.69 s on 1024 cores. Figure 2 shows only a 26% increase in …

… In the second chapter, we review MsFEM for solving partial differential equations with
multiscale solutions; see [145, 147, 146, 107, 71, 260, 14, 103]. The central goal of this approach …