A discrete element method representation of an anisotropic elastic continuum

A Nearly Analytic Discrete Method for Acoustic and Elastic Wave Equations in Anisotropic Media

We transform the seismic wave equations in 2D inhomogeneous anisotropic media into a system of first-order partial differential equations with respect to time t. Based on the transformed equations, a new nearly analytic discrete method (NADM) is developed in this article. Our method enables wave propagation to be simulated in two dimensions through generally anisotropic and heterogeneous models...

Stress Analysis of 3D Generally Anisotropic Elastic Solids Using the Boundary Element Method

The explicit, closed-form expressions of the Green’s functions for generally anisotropic elastic solids in three-dimensions that have been derived using Stroh’s formalism are employed in a formulation of the boundary element method (BEM). Unlike several other existing schemes, the evaluation of these fundamental solutions does not require further numerical integration in the BEM algorithm; they...

Accepted Manuscript a Constrained Finite Element Method Satisfying the Discrete Maximum Principle for Anisotropic Diffusion Problems

Nonlinear constrained finite element approximations to anisotropic diffusion problems are considered. Starting with a standard (linear or bilinear) Galerkin discretization, the entries of the stiffness matrix are adjusted so as to enforce sufficient conditions of the discrete maximum principle (DMP). An algebraic splitting is employed to separate the contributions of negative and positive off-d...

A Crack in an Anisotropic Elastic Slab*

A constrained finite element method satisfying the discrete maximum principle for anisotropic diffusion problems

Nonlinear constrained finite element approximations to anisotropic diffusion problems are considered. Starting with a standard (linear or bilinear) Galerkin discretization, the entries of the stiffness matrix are adjusted so as to enforce sufficient conditions of the discrete maximum principle (DMP). An algebraic splitting is employed to separate the contributions of negative and positive off-d...