Iterative solution of isoparametric spectral element equations by low-order finite element preconditioning

Solution of Wave Equations Near Seawalls by Finite Element Method

A 2D finite element model for the solution of wave equations is developed. The fluid is considered as incompressible and irrotational. This is a difficult mathematical problem to solve numerically as well as analytically because the condition of the dynamic boundary (Bernoulli’s equation) on the free surface is not fixed and varies with time. The finite element technique is applied to solve non...

Finite Element Preconditioning on Spectral Element Discretizations for Coupled Elliptic Equations

Solution of Noncatalytic Packed Bed Reactors Equations by Finite Element Method

Finite-Element Preconditioning of G-NI Spectral Methods

Several old and new finite-element preconditioners for nodal-based spectral discretizations of −∆u = f in the domain Ω = (−1, 1) (d = 2 or 3), with Dirichlet or Neumann boundary conditions, are considered and compared in terms of both condition number and computational efficiency. The computational domain covers the case of classical single-domain spectral approximations (see [5]), as well as t...

A numerical experimental study of inverse preconditioning for the parallel iterative solution to 3D finite element flow equations

Integration of the subsurface flow equation by finite elements (FE) in space and finite differences (FD) in time requires the repeated solution to sparse symmetric positive definite systems of linear equations. Iterative techniques based on preconditioned conjugate gradients (PCG) are one of the most attractive tool to solve the problem on sequential computers.A present challenge is to make PCG...