This paper is concerned with a multi-domain spectral method, based on an interior penalty discontinuous Galerkin (IPDG) formulation, for the exterior Helmholtz problem truncated via an exact circular or spherical Dirichlet-to-Neumann (DtN) boundary condition. An effective iterative approach is proposed to localize the global DtN boundary condition, which facilitates the implementation of multi-domain methods, and the treatment for complex geometry of the scatterers. Under a discontinuous Galerkin formulation, the proposed method allows to use polynomial basis functions of different degree on different subdomains, and more importantly, explicit wave number dependence estimates of the spectral scheme can be derived, which is somehow implausible for a multi-domain continuous Galerkin formulation.  

The aim of the electron microscopy image classification is to categorize the projection images into different classes according to their similarities. Distinguishing images usually requires that these images are aligned first. However, alignment of images is a difficult task for a highly noisy data set. In this paper, we propose a translation and rotation invariant based on the Fourier transform for avoiding alignment. A novel classification method is therefore established. To accelerate the classification speed, secondary-classes are introduced in the classification process. The test results also show that our method is very efficient and effective. Classification results using our invariant are also compared with the results using other existing invariants, showing that our invariant leads to much better results.

In this paper, by combining the second order characteristics time discretization with the variational multiscale finite element method in space we get a second order modified characteristics variational multiscale finite element method for the time dependent Navier-Stokes problem. The theoretical analysis shows that the proposed method has a good convergence property. To show the efficiency of the proposed finite element method, we first present some numerical results for analytical solution problems. We then give some numerical results for the lid-driven cavity flow with $Re$=5000, 7500 and 10000. We present the numerical results as the time is sufficiently long, so that the steady state numerical solutions can be obtained.

In this paper we modify the MEBDF method using the NDFs as predictors instead of the BDFs. We have done it in three different ways: changing both predictors of the MEBDF, changing only the first predictor and changing only the second one. We have called the new methods MENDF, MENBDF and MEBNDF respectively. The new methods are A-stable up to order $4$ and the stability properties of the new methods are better than the MEBDF method.

In this paper, we present an accelerated simulation approach on waveform relaxation using Krylov subspace for a large time-dependent system composed of some subsystems. This approach first allows these subsystems to be decoupled by waveform relaxation. Then the Arnoldi procedure based on Krylov subspace is provided to accelerate the simulation of the decoupled subsystems independently. For the new approach, the convergent conditions on waveform relaxation are derived. The robust behavior is also successfully illustrated via numerical examples.

This work is concerned with the nonlinear matrix equation $X^s + A^*F(X)A= Q$ with $s ≥ 1$. Several sufficient and necessary conditions for the existence and  uniqueness of the Hermitian positive semidefinite solution are derived, and perturbation bounds are presented.