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In this talk, we introduce the so-called inverse Lax-Wendroff (ILW) boundary treatment for finite difference approximations on the Cartesian mesh. As the domain boundary may intersect with the grid in...
In this talk we will review some recent results on space-time finite and boundary element methods for the wave equation. As a first model problem we consider the inhomogeneous wave equation with zero ...
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...
Wan and Zhang have recently obtained a nontrivial lower bound for the number of zeros of complete symmetric polynomials over finite fields, and proposed a problem whether their bound can be improved. ...
We propose two families of nonconforming finite elements on $n$-rectangle meshes of any dimension to solve the sixth-order elliptic equations. The unisolvent property and the approximation ability of ...
A difference field is a field with a distinguished automorphism. Automorphisms of a finite field are powers of the Frobenius map. In this talk, I will discuss how to estimate the number of rational po...
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...
Let G be a finite abelian group. If f: G → C is a nonzero function with Fourier transform f , the Donoho-Stark uncertainty principle states that|supp(f)||supp(f )|≥|G|. The purpose of this talk is two...
Landau-Lifshitz-Gilbert equation (LLG) describes magnetization of ferromagnets. In this paper, we consider the singularity formation of LLG from R^2 to S^2. For any prescribed N distinct points q^{j} ...
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,...
D-finite functions are solutions of homogeneous linear differential equations with rational function coefficients. This is an important class of special functions since it appears ubiquitously in alge...
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...
I will present the joint work with Jialun Li and Pratyush Sarkar in the talk. As a final work to establish that the frame flows for geometrically finite hyperbolic manifolds of arbitrary dimensions ar...
I will present the joint work with Jialun Li and Pratyush Sarkar in the talk. As a final work to establish that the frame flows for geometrically finite hyperbolic manifolds of arbitrary dimensions ar...
Multiscale phenomena significantly impact on the computation and modeling for scientific and engineering problems. Multiscale finite element methods are used to build reduced order computational model...

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