Fast finite-difference solution of biharmonic problems

A Fundamental Solution for a Biharmonic Finite-Difference Operator1

Sinc Solution of Biharmonic Problems

In this paper we solve two biharmonic problems over a square, B = (−1, 1) × (−1, 1). (1) The problem ∇4U = f , for which we determine a particular solution, U , given f , via use of Sinc convolution; and (2) The boundary value problem ∇4V = 0 for which we determine V given V = g and normal derivative Vn = h on ∂B, the boundary of B. The solution to this problem is carried out based on the identity

Finite Difference Solution of Mixed Boundary-value Elastic Problems

A new numerical method of solution has been developed for the analysis of deformation and stresses in elastic bodies subjected to mixed boundary-conditions. The program is capable of dealing with both regular and irregular shapes of boundaries appropriately. An ideal mathematical model, based on the displacement potential function, has been used in the finite difference solution. The present pa...

A fast finite difference method for biharmonic equations on irregular domains

Biharmonic equations have many applications, especially in fluid and solid mechanics, but difficult to solve due to the fourth order derivatives in the differential equation. In this paper a fast second order accurate algorithm based on a finite difference discretization and a Cartesian grid is developed for two dimensional biharmonic equations on irregular domains with essential boundary condi...

Significant Error Propagation in the Finite Difference Solution of Non-Linear Magnetostatic Problems Utilizing Boundary Condition of the Third Kind

This paper poses two magnetostatic problems in cylindrical coordinates with different permeabilities for each region. In the first problem the boundary condition of the second kind is used while in the second one, the boundary condition of the third kind is utilized. These problems are solved using the finite element and finite difference methods. In second problem, the results of the finite di...