Related papers: A N-Body Solver for Free Mesh Interpolation
A major obstacle to the application of the standard Radial Basis Function-generated Finite Difference (RBF-FD) meshless method is constituted by its inability to accurately and consistently solve boundary value problems involving Neumann…
We present a generalization of the RBF-FD method that computes RBF-FD weights in finite-sized neighborhoods around the centers of RBF-FD stencils by introducing an overlap parameter $\delta \in [0,1]$ such that $\delta=1$ recovers the…
In this paper, we introduce a superconvergent approximation method that employs radial basis functions (RBFs) in the numerical solution of conservation laws. The use of RBFs for interpolation and approximation is a well developed area of…
We present simpler algorithms for two closely related morphing problems, both based on the barycentric interpolation paradigm introduced by Floater and Gotsman, which is in turn based on Floater's asymmetric extension of Tutte's classical…
We propose a novel numerical approach to separate multiple tissue compartments in image voxels and to estimate quantitatively their nuclear magnetic resonance (NMR) properties and mixture fractions, given magnetic resonance fingerprinting…
We present a quasi-linearly scaling, first order polynomial finite element method for the solution of the magnetostatic open boundary problem by splitting the magnetic scalar potential. The potential is determined by solving a Dirichlet…
Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted…
We discuss interrelations between: Cohn localizations of full square matrices; a Leavitt localization of a row; and the Jacobson quasi-inverses of quasi-regular elements. The latter Jacobson localizations appear naturally and easily in…
Exploiting the variational interpretation of kernel interpolation we exhibit a direct connection between interpolation and regression, where interpolation appears as a limiting case of regression. By applying this framework to point clouds…
The use of the Factorization method for Electrical Impedance Tomography has been proved to be very promising for applications in the case where one wants to find inhomogeneous inclusions in a known background. In many situations, the…
In this work, the matrix-free solution of quasi-static phase-field fracture problems is further investigated. More specifically, we consider a quasi-monolithic formulation in which the irreversibility constraint is imposed with a…
This work studies shape filtering techniques, namely the convolution-based (explicit) and the PDE-based (implicit), and introduces an implicit bulk-surface filtering method to control the boundary smoothness and preserve the internal mesh…
A fundamental macroscopic description of a magnetized plasma is the Vlasov equation supplemented by the nonlinear inverse-square force Fokker-Planck collision operator [Rosenbluth et al., Phys. Rev., 107, 1957]. The Vlasov part describes…
We present new calculations of the energy flux of a spinning test-body on circular orbits around a Schwarzschild black hole at linear order in the particle spin. We compute the multipolar fluxes up to $\ell=m=6$ using two independent…
We present a novel method to model and calculate deformation fields between shapes embedded in $\mathbb{R}^D$. Our framework combines naturally interpolating the two input shapes and calculating correspondences at the same time. The key…
We are interested in mesh-free formulas based on the Monte-Carlo methodology for the approximation of multi-dimensional integrals, and we investigate their accuracy when the functions belong to a reproducing-kernel space. A kernel typically…
We present a spectrally accurate fast algorithm for evaluating the solution to the scalar wave equation in free space driven by a large collection of point sources in a bounded domain. With $M$ sources temporally discretized by $N_t$ time…
The nonlinear force-free field (NLFFF) model is often used to describe the solar coronal magnetic field, however a series of earlier studies revealed difficulties in the numerical solution of the model in application to photospheric…
This note carries three purposes involving our latest advances on the radial basis function (RBF) approach. First, we will introduce a new scheme employing the boundary knot method (BKM) to nonlinear convection-diffusion problem. It is…
Parametric model order reduction (pMOR) is a powerful tool for accelerating finite element (FE) simulations while maintaining parametric dependencies. For geometric parameters, pMOR by matrix interpolation is a well-suited approach because…