Related papers: A well conditioned Method of Fundamental Solutions
In recent years, a variety of meshless methods have been developed to solve partial differential equations in complex domains. Meshless methods discretize the partial differential equations over scattered points instead of grids. Radial…
We discuss exact analytical solutions of a variety of statistical models recently obtained for finite systems by a novel powerful mathematical method, the Laplace-Fourier transform. Among them are a constrained version of the statistical…
We report on the possibilities of using the method of normal fundamental systems for solving some problems of oscillation theory. Large elastic dynamical systems with continuous and discrete parameters are considered, which have many…
We present the general forms of piece-wise functions on partitioned domains satisfying an intrinsic $C^0$ or $C^1$ continuity across the sub-domain boundaries. These general forms are constructed based on a strategy stemming from the theory…
The problem of increasing the accuracy of an approximate solution is considered for boundary value problems for parabolic equations. For ordinary differential equations (ODEs), nonstandard finite difference schemes are in common use for…
Exceptionally elegant formulae exist for the fractional Laplacian operator applied to weighted classical orthogonal polynomials. We utilize these results to construct a solver, based on frame properties, for equations involving the…
Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…
A conformal flattening maps a curved surface to the plane without distorting angles---such maps have become a fundamental building block for problems in geometry processing, numerical simulation, and computational design. Yet existing…
This paper introduces a fast and numerically stable algorithm for the solution of fourth-order linear boundary value problems on an interval. This type of equation arises in a variety of settings in physics and signal processing. Our method…
Solving partial differential equations (PDEs) with highly oscillatory solutions on complex domains remains a challenging and important problem. High-frequency oscillations and intricate geometries often result in prohibitively expensive…
Complex processes in perforated domains occur in many real-world applications. These problems are typically characterized by physical processes in domains with multiple scales (see Figure 1 for the illustration of a perforated domain).…
Periodic micromagnetic finite element method (PM-FEM) is introduced to solve periodic unit cell problems using the Landau-Lifshitz-Gilbert equation. PM-FEM is applicable to general problems with 1D, 2D, and 3D periodicities. PM-FEM is based…
In this paper, we study a class of nonsmooth fractional programs {\rm (FP, for short)} with SOS-convex semi-algebraic functions. Under suitable assumptions, we derive a strong duality result between the problem (FP) and its semidefinite…
Non-negative matrix factorization (NMF) is a recently developed technique for finding parts-based, linear representations of non-negative data. Although it has successfully been applied in several applications, it does not always result in…
This paper presents a novel mass-conservative mixed multiscale method for solving flow equations in heterogeneous porous media. The media properties (the permeability) contain multiple scales and high contrast. The proposed method solves…
Several multiscale methods account for sub-grid scale features using coarse scale basis functions. For example, in the Multiscale Finite Volume method the coarse scale basis functions are obtained by solving a set of local problems over…
An efficient numerical method is proposed for computing the Dirichlet-to-Neumann (DtN) map associated with the exterior Dirichlet problem for the two-dimensional Helmholtz equation with an inhomogeneous term. The exterior solution is…
We focus on the initial boundary value problem for a general scalar balance law in one space dimension. Under rather general assumptions on the flux and source functions, we prove the well-posedness of this problem and the stability of its…
Factorization machine (FM) variants are widely used for large scale real-time content recommendation systems, since they offer an excellent balance between model accuracy and low computational costs for training and inference. These systems…
Many modern datasets, from areas such as neuroimaging and geostatistics, come in the form of a random sample of tensor-valued data which can be understood as noisy observations of a smooth multidimensional random function. Most of the…