Chin-Tien Wu

Analysis and Comparison of Geometric and Algebraic Multigrid for Convection-Diffusion Equations

The discrete convection-diffusion equations obtained from streamline diffusion finite element discretization are solved on both uniform meshes and adaptive meshes. Estimates of error reduction rates for both geometric multigrid (GMG) and algebraic multigrid (AMG) are established on uniform rectangular meshes for a model problem. Our analysis shows that GMG with line Gauss-Seidel smoothing and bilinear interpolation converges if

Structure-preserving Arnoldi-type algorithm for solving eigenvalue problems in leaky surface wave propagation

h\gg \epsilon^{2/3}

An Efficient Energy Minimization for Conformal Parameterizations

, and AMG with the same smoother converges more rapidly than GMG if the interpolation constant

A Novel Stretch Energy Minimization Algorithm for Equiareal Parameterizations

\beta

An approach to construct freeform surface by solving Monge-Ampere equation

in the approximation assumption of AMG satisfies

New approach to construct freeform surface by numerically differential formulation

\beta \ll (\frac{h}{\sqrt{\epsilon}})^{\alpha}, \hs{1mm} \mbox{where

Vibration of fast trains, palindromic eigenvalue problems and structure-preserving doubling algorithms

\alpha = \Big\{ {\begin{smallmatrix} 1, & {h < \sqrt \varepsilon, } \\ 2, & {h \ge \sqrt \varepsilon.} \\ \end{smallmatrix}}

Palindromic eigenvalue problems: A brief survey

}

ADAPTIVE MESH REFINEMENT FOR ELLIPTIC INTERFACE PROBLEMS USING THE NON-CONFORMING IMMERSED FINITE ELEMENT METHOD

On unstructured triangular meshes, the performance of GMG and AMG, both as solvers and as preconditioners for GMRES, are evaluated. Numerical results show that GMRES with AMG preconditioning is a robust and reliable solver on both type of meshes.

Reconstruction of inclusions in an elastic body

We study the generalized eigenvalue problems (GEPs) that arise from modeling leaky surface wave propagation in an acoustic resonator with an infinite amount of periodically arranged interdigital transducers. The constitutive equations are discretized by finite element methods with mesh refinements along the electrode interfaces and corners. The nonzero eigenvalues of the resulting GEP appear in reciprocal pairs (@l,1/@l). We transform the GEP into a T-palindromic quadratic eigenvalue problem (TPQEP) to reveal the important reciprocal relationships of the eigenvalues. The TPQEP is then solved by a structure-preserving algorithm incorporating a generalized T-skew-Hamiltonian implicitly restarted Arnoldi method so that the reciprocal relationship of the eigenvalues may be automatically preserved. Compared with applying the Arnoldi method to solve the GEPs, our numerical results show that the eigenpairs produced by the proposed structure-preserving method not only preserve the reciprocal property but also possess high efficiency and accuracy.