David Da-Kwun Chien

Piecewise polynomial collocation for boundary integral equations

This paper considers the numerical solution of boundary integral equations of the second kind for Laplace’s equation

A spectral method for elliptic equations: the Dirichlet problem

\Delta u = 0

A spectral method for elliptic equations: the Neumann problem

on connected regions D in

A fast matrix–vector multiplication method for solving the radiosity equation

{\bf R}^3

Evaluating polynomials over the unit disk and the unit ball

with boundary S. The boundary S is allowed to be smooth or piecewise smooth, and we let

A spectral method for parabolic differential equations

\{ \Delta _K |1 \leq K \leq N\}

A spectral method for nonlinear elliptic equations

be a triangulation of S. The numerical method is collocation with approximations which are piecewise quadratic in the parametrization variables, leading to a numerical solution

Phase retrieval from integrated near-field diffraction intensity

u_N

A spectral method for an elliptic equation with a nonlinear Neumann boundary condition

. Superconvergence results for

A Spectral Method for the Biharmonic Equation

u_N