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In this paper, we present how high-order accurate solutions to elliptic partial differential equations can be achieved in arbitrary spatial domains using radial basis function-generated finite differences (RBF-FD) on unfitted node sets…
It is demonstrated that non-constant kernel solution, that can fit the spatial variations of the kernel can be obtained with minimum computing time. The CPU cost required with this new extension of the image subtraction method is almost the…
Multiple solutions are common in various non-convex problems arising from industrial and scientific computing. Nonetheless, understanding the nontrivial solutions' qualitative properties seems limited, partially due to the lack of efficient…
Strong-form meshless methods received much attention in recent years and are being extensively researched and applied to a wide range of problems in science and engineering. However, the solution of elasto-plastic problems has proven to be…
Generalizing the well-known relations on characteristic functions on a plane to the case of a one-dimensional regular surface (curve) with compact support, we establish implicit equations for these functions. Introducing an approximation,…
Numerical solutions of partial differential equations (PDEs) on manifolds continues to generate a lot of interest among scientists in the natural and applied sciences. On the other hand, recent developments of 3D scanning and computer…
For the Poisson equation posed in a domain containing a large number of polygonal perforations, we propose a low-dimensional coarse approximation space based on a coarse polygonal partitioning of the domain. Similarly to other multiscale…
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…
A mixed basis approach based on density functional theory is extended to one-dimensional(1D) systems. The basis functions here are taken to be the localized B-splines for the two finite non-periodic dimensions and the plane waves for the…
A radial basis function (RBF) method based on matrix-valued kernels is presented and analyzed for computing two types of vector decompositions on bounded domains: one where the normal component of the divergence-free part of the field is…
We investigate nonlinear, higher-order dispersive equations with measure (or even less regular) potentials and initial data with low regularity. Our approach is of distributional nature and relies on the phase space analysis (via Gabor wave…
We present an efficient implementation of a surface Green's-function method for atomistic modeling of surfaces within the framework of density functional theory using a pseudopotential localized basis set approach. In this method, the…
We study the Cowling approximation by analytical means as applied to a system of linear differential equations arising from models of non-radial stellar pulsation. We consider various asymptotic cases, including those of high harmonic…
A Radial Basis Function Generated Finite-Differences (RBF-FD) inspired technique for evaluating definite integrals over bounded volumes that have smooth boundaries in three dimensions is described. A key aspect of this approach is that it…
We study subharmonic functions whose Laplacian is supported on a null set and in connected components of of the complement to the support admit harmonic extensions to larger sets. We prove that if such a function has a piecewise holomorphic…
The first part of this work established the foundations of a radial duality between nonnegative optimization problems, inspired by the work of (Renegar, 2016). Here we utilize our radial duality theory to design and analyze projection-free…
In this paper we propose and analyze a new Multiscale Method for solving semi-linear elliptic problems with heterogeneous and highly variable coefficient functions. For this purpose we construct a generalized finite element basis that spans…
A method for the fast and accurate solution of the radiative transfer equation in plane-parallel media with coherent isotropic scattering is presented. This largely analytical approach uses the formalism of meromorphic functions in order to…
Isolated patches of spatially oscillating pattern have been found to emerge near a pattern-forming instability in a wide variety of experiments and mathematical models. However, there is currently no mathematical theory to explain this…
Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order models of parametrized partial differential equation problems. With speedups that can reach several orders of…