相关论文: A fast multipole method for the evaluation of elas…

This paper reviews standard oversampling strategies as performed in the Multiscale Finite Element Method (MsFEM). Common to those approaches is that the oversampling is performed in the full space restricted to a patch but including coarse…

For the Lagrange interpolation over a triangular domain, we propose an efficient algorithm to rigorously evaluate the interpolation error constant under the maximum norm by using the finite element method (FEM). In solving the optimization…

In this article, a fast algorithm based on time two-mesh (TT-M) finite element (FE) scheme, which aims at solving nonlinear problems quickly, is considered to numerically solve the nonlinear space fractional Allen-Cahn equations with smooth…

A positivity-preserving fractional algorithm is presented for solving the four-equation homogeneous relaxation model (HRM) with an arbitrary number of ideal gases and a liquid governed by the stiffened gas equation of state. The fractional…

From a mathematical perspective, the extraordinary properties of metamaterials are often reflected in the coefficients of the governing partial differential equations (PDEs). These coefficients may fall outside the assumptions of classical…

We propose a general method to obtain the scalar worldline Green function on an arbitrary 1D topological space, with which the first-quantized method of evaluating 1-loop Feynman diagrams can be generalized to calculate arbitrary ones. The…

With current observational methods it is not possible to directly measure the magnetic field in the solar corona with sufficient accuracy. Therefore, coronal magnetic field models have to rely on extrapolation methods using photospheric…

The oversampling multiscale finite element method (MsFEM) is one of the most popular methods for simulating composite materials and flows in porous media which may have many scales. But the method may be inapplicable or inefficient in some…

We describe a new, adaptive solver for the two-dimensional Poisson equation in complicated geometries. Using classical potential theory, we represent the solution as the sum of a volume potential and a double layer potential. Rather than…

Inverse design enables automating the discovery and optimization of devices achieving performance significantly exceeding that of traditional human-engineered designs. However, existing methodologies to inverse-design electromagnetic…

Purpose: Previously-developed Voxel Spread Function (VSF) method (Yablonskiy, et al, MRM, 2013;70:1283) provides means to correct artifacts induced by macroscopic magnetic field inhomogeneities in the images obtained by…

The Kohn-Sham method uses a single model system, and corrects it by a density functional the exact user friendly expression of which is not known and is replaced by an approximated, usable, model. We propose to use instead more than one…

In this paper, we present a generalization of the classical error bounds of Greengard-Rokhlin for the Fast Multipole Method (FMM) for Laplace potentials in three dimensions, extended to the case of local expansion (instead of point)…

We present a spectrally accurate, efficient FFT-based method for the three-dimensional free-space Poisson equation with smooth, compactly supported sources. The method adopts a super-potential formulation: we first compute the convolution…

This work presents an abstract framework for the design, implementation, and analysis of the multiscale spectral generalized finite element method (MS-GFEM), a particular numerical multiscale method originally proposed in [I. Babuska and R.…

The popular, stable, robust and computationally inexpensive cubic spline interpolation algorithm is adopted and used for finite temperature Green's function calculations of realistic systems. We demonstrate that with appropriate…

For the extrapolation of magnetic fields into the solar corona from measurements taken in the photosphere (or chromosphere) force-free magnetic fields are typically used. This does not take into account that the lower layers of the solar…

A new approximation method for inverting the Poisson's equation is presented for a continuously distributed and finite-sized source in an unbound domain. The advantage of this image multipole method arises from its ability to place the…

The fundamental solution (Green function) for the Cauchy problem of the space-time fractional diffusion equation is investigated with respect to its scaling and similarity properties, starting from its Fourier-Laplace representation. Then,…

Nonlinear energy functionals appearing in the calculus of variations can be discretized by the finite element (FE) method and formulated as a sum of energy contributions from local elements. A fast evaluation of energy functionals…