Shubin Fu

A time explicit multiscale framework for heterogeneous elastic wave propagation based on multipoint stress discretization

Xiang Zhong, Eric T. Chung, Shubin Fu

Simulating elastic wave propagation in heterogeneous media presents significant mathematical and computational challenges, since resolving fine-scale material variations requires extremely fine spatial discretizations, while mixed stress--displacement formulations typically lead to large saddle-point systems that are not well suited for efficient time integration. …

A time explicit multiscale framework for heterogeneous elastic wave propagation based on multipoint stress discretization

Xiang Zhong, Eric T. Chung, Shubin Fu

Simulating elastic wave propagation in heterogeneous media presents significant mathematical and computational challenges, since resolving fine-scale material variations requires extremely fine spatial discretizations, while mixed stress--displacement formulations typically lead to large saddle-point systems that are not well suited for efficient time integration. …

hk, cn (code pays fourni par la source)

A Fully Matrix-Free Three-Grid Preconditioner for the Time-Harmonic Maxwell Equations at Extreme Scale

Shubin Fu

Three-dimensional time-harmonic Maxwell simulations generate massive complex indefinite systems whose mesh coarsening is strictly limited by phase accuracy. Although matrix-free finite element kernels utilize GPU throughput efficiently, standard multilevel solvers are ultimately bottlenecked by the memory and communication costs of exact coarse-grid …

A Massively Parallel Three-Grid Preconditioner for the High-Frequency Helmholtz Equation

Shubin Fu, Yitong Wang, Zixiao Zhao

Accurate simulation of three-dimensional time-harmonic wave propagation over many wavelengths requires control of phase error and efficient solution of large indefinite systems. We develop a three-grid solver based on the compact 27-point interpolated optimized finite-difference (IOFD) discretization. Its wavenumber-dependent stencil supports a …

Edge Multiscale Finite Element Methods

Shubin Fu, Guanglian Li

The objective of this paper is to review recent developments in Edge Multiscale Finite Element Methods (EMsFEM) for partial differential equations with heterogeneous coefficients or highly oscillatory solutions. Using elliptic equations with heterogeneous coefficients as an illustrative example, we present the key …

Edge Multiscale Finite Element Methods

Shubin Fu, Guanglian Li

The objective of this paper is to review recent developments in Edge Multiscale Finite Element Methods (EMsFEM) for partial differential equations with heterogeneous coefficients or highly oscillatory solutions. Using elliptic equations with heterogeneous coefficients as an illustrative example, we present the key …

hk (code pays fourni par la source)

An adaptive two-grid preconditioner and linearly implicit scheme for shale gas transport in fractured porous media

Maria Vasilyeva, Ben S. Southworth, Shubin Fu

Abstract We consider a nonlinear mixed-dimensional model for simulating gas transport in shale formation. The mathematical model consists of a coupled system of nonlinear equations, where flow within fractures is represented using a lower-dimensional representation. For the numerical solution of the coupled …

us (code pays fourni par la source)

An algebraic multiscale preconditioner for large sparse SPD matrices

Yingjie Zhou, Shubin Fu, Eric Tsz Shun Chung

We present a two-grid algebraic multiscale preconditioner for large sparse symmetric positive definite systems arising from elliptic problems with highly heterogeneous coefficients. The coarse space is constructed directly from the system matrix by graph partitioning and local generalized eigenvalue solvers, yielding basis …

An algebraic multiscale preconditioner for large sparse SPD matrices

Yingjie Zhou, Shubin Fu, Eric Tsz Shun Chung

We present a two-grid algebraic multiscale preconditioner for large sparse symmetric positive definite systems arising from elliptic problems with highly heterogeneous coefficients. The coarse space is constructed directly from the system matrix by graph partitioning and local generalized eigenvalue solvers, yielding basis …

hk (code pays fourni par la source)

Applying Two-Grid Preconditioner for Subsurface Flow Simulation using Attention-enhanced Hybrid Network to Accelerate Multiscale Discretization in High-contrast Media

Peiqi Li, Jie Chen (5892), Shubin Fu

In this paper, we study the efficient numerical solution of Darcy equations in strongly heterogeneous media with high-contrast permeability and propose a hybrid framework that combines learning with multiscale numerical methods. The learning component is used for the prediction of multiscale basis …

Applying Two-Grid Preconditioner for Subsurface Flow Simulation using Attention-enhanced Hybrid Network to Accelerate Multiscale Discretization in High-contrast Media

Peiqi Li, Jie Chen (5892), Shubin Fu

In this paper, we study the efficient numerical solution of Darcy equations in strongly heterogeneous media with high-contrast permeability and propose a hybrid framework that combines learning with multiscale numerical methods. The learning component is used for the prediction of multiscale basis …

gb, cn, nz (code pays fourni par la source)