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Phononic crystals are composite materials with periodic distribution of two or more media. The difficulty of computing the band structure of the phononic crystals lies in capturing the complex geometr...
In this talk, I begin with a review of different geometric flows (PDEs) including mean curvature (curve shortening) flow,surface diffusion flow, Willmore flow, etc., which arise from materials science...
An unfitted interface penalty finite element method is proposed for the interface problems, in which Nitsche's method together with the ideas of merging elements and harmonic weighing fluxes are used,...
In this talk, we present numerical approximations of a phase-field model for two-phase ferrofluids, which consists of the Navier-Stokes equations, the Cahn-Hilliard equation, the magnetostatic equatio...
In this talk, we present numerical approximations of a phase-field model for two-phase ferrofluids, which consists of the Navier-Stokes equations, the Cahn-Hilliard equation, the magnetostatic equatio...
We present a mixednite element method for a model of the flow in a Hele-Shaw cell of 2-D fluid droplets surrounded by air driven by surface tension and actuated by an electric &...
We reformulate an extended finite element (FE) framework for embedded frictional cracks in elastoplastic solids to accommodate finite deformation, including finite stretching and rotation. For the FE ...
Contact problem suffers from a numerical instability similar to that encountered in incompressible elasticity, in which the normal contact pressure exhibits spurious oscillation. This oscillation does...
We present an incremental quasi-static contact algorithm for path-dependent frictional crack propagation in the framework of the extended finite element (FE) method. The discrete formulation allows fo...
Modern semiconductor manufacturing requires photolithographic printing of subillumination wavelength features in photoresist via electromagnetic energy scattered by complicated photomask designs. This...
Based on H1-Galerkin mixed finite element method with nonconforming quasi-Wilson element, a numerical approximate scheme is established for pseudo-hyperbolic equations under arbitrary quadrilateral me...
In an earlier paper, we presented an iterative algorithm for reconstructing a three dimensional density function from a set of two dimensional electron microscopy images. By minimizing an energy fun...
In this paper, we present a novel L2-gradient flow based semi-implicit finite element method for solving a variational model of image reconstruction under various data scenarios, especially for the ...
We propose a condition under which the heterogeneous multiscale ite element method converges for elliptic problem with nonsmooth coe眂ients, and obtain the optimal convergence rate for elliptic prob...
In this paper, we develop an adaptive finite element method based on reliable and efficient a posteriori error estimates for the H formulation of eddy current problems with multiply connec...

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