Related papers: Numerical Stability on Local Integral Methods usin…
In this paper, a new implicit-explicit local method with an arbitrary order is produced for stiff initial value problems. Here, a general method for one-step time integrations has been created, considering a direction free approach for…
In this paper, a piecewise quadratic nonconforming finite element method on rectangular grids for a fourth-order elliptic singular perturbation problem is presented. This proposed method is robustly convergent with respect to the…
Based on the radial basis function (RBF), non-singular general solution and dual reciprocity principle (DRM), this paper presents an inheretnly meshless, exponential convergence, integration-free, boundary-only collocation techniques for…
For radial basis function (RBF) kernel interpolation of scattered data, Schaback in 1995 proved that the attainable approximation error and the condition number of the underlying interpolation matrix cannot be made small simultaneously. He…
This work develops advanced numerical methods for free-surface simulations of polymer mixing processes, integrating a Volume of Fluid (VOF) interface-capturing approach with a non-conforming Immersed Boundary (IB) method to model two-phase…
In this work it is shown how the immersed boundary method of (Peskin2002) for modeling flexible structures immersed in a fluid can be extended to include thermal fluctuations. A stochastic numerical method is proposed which deals with…
Atkinson developed a strategy which splits solution of a PDE system into homogeneous and particular solutions, where the former have to satisfy the boundary and governing equation, while the latter only need to satisfy the governing…
The purpose of this study is to apply some new RBF collocation schemes and recently-developed kernel RBFs to various types of partial differential equation systems. By analogy with the Fasshauer's Hermite interpolation, we recently…
In this paper, we discuss the problem of constructing Radial Basis In this paper, we discuss the problem of constructing Radial Basis Function (RBF)-based Partition of Unity (PU) interpolants that are positive if data values are positive.…
In this paper we describe a parallel implicit method based on radial basis functions (RBF) for surface reconstruction. The applicability of RBF methods is hindered by its computational demand, that requires the solution of linear systems of…
We propose a high-precision numerical quadrature framework based on local Fourier extension (LFE) approximations. The method constructs, on each subinterval, a truncated-SVD stabilized local Fourier continuation of the integrand on an…
The immersed boundary-finite element method (IBFE) is an approach to describing the dynamics of an elastic structure immersed in an incompressible viscous fluid. In this formulation, there are discontinuities in the pressure and viscous…
This paper concerns the inverse scattering problem to reconstruct a locally perturbed periodic surface. Different from scattering problems with quasi-periodic incident fields and periodic surfaces, the scattered fields are no longer…
The Immersed Boundary (IB) method is a mathematical framework for constructing robust numerical methods to study fluid-structure interaction in problems involving an elastic structure immersed in a viscous fluid. The IB formulation uses an…
In this paper, we propose a novel image interpolation algorithm, which is formulated via combining both the local autoregressive (AR) model and the nonlocal adaptive 3-D sparse model as regularized constraints under the regularization…
In this paper, our objective is primarily to use adaptive inverse-quadratic (IQ) and inverse-multi-quadratic (IMQ) radial basis function (RBF) interpolation techniques to develop an enhanced Adam-Bashforth and Adam-Moulton methods. By…
In this paper we present a locally and dimension-adaptive sparse grid method for interpolation and integration of high-dimensional functions with discontinuities. The proposed algorithm combines the strengths of the generalised sparse grid…
In this paper, we examine a number of additive and multiplicative multilevel iterative methods and preconditioners in the setting of two-dimensional local mesh refinement. While standard multilevel methods are effective for uniform…
In this paper, we propose a new trigonometric interpolation algorithm and establish relevant convergent properties. The method adjusts an existing trigonometric interpolation algorithm such that it can better leverage Fast Fourier Transform…
In this paper, we propose a multiscale empirical interpolation method for solving nonlinear multiscale partial differential equations. The proposed method combines empirical interpolation techniques and local multiscale methods, such as the…