Related papers: Streamline integration as a method for structured …
We propose a new numerical algorithm to construct a structured numerical elliptic grid of a doubly connected domain. Our method is applicable to domains with boundaries defined by two contour lines of a two-dimensional function. The…
Calculating dynamical diffraction patterns for X-ray topography and similar x-ray scattering-imaging techniques require the numerical integration of the Takagi-Taupin equations. This is usually performed with a simple second order finite…
A Cartesian grid method combined with a simplified gas kinetic scheme is presented for subsonic and supersonic viscous flow simulation on complex geometries. Under the Cartesian mesh, the computational grid points are classified into four…
In this work, an efficient blackbox-type multigrid method is proposed for solving multipoint flux approximations of the Darcy problem on logically rectangular grids. The approach is based on a cell-centered multigrid algorithm, which…
We present a novel de-homogenization approach for efficient design of high-resolution load-bearing structures. The proposed approach builds upon a streamline-based parametrization of the design domain, using a set of space-filling and…
In this paper, we study FPGA based pipelined and superscalar design of two variants of conjugate gradient methods for solving Laplacian equation on a discrete grid; the first version corresponds to the original conjugate gradient algorithm,…
A numerical method is proposed in order to track field lines of three-dimensional divergence free fields. Field lines are computed by a locally valid Hamiltonian mapping, which is computed using a symplectic scheme. The method is…
We present a hybrid particle/grid approach for simulating incompressible fluids on collocated velocity grids. We interchangeably use particle and grid representations of transported quantities to balance efficiency and accuracy. A novel…
In [L. Chen and R. Li, Journal of Scientific Computing, Vol. 68, pp. 1172--1197, (2016)], an integrated linear reconstruction was proposed for finite volume methods on unstructured grids. However, the geometric hypothesis of the mesh to…
We present novel families of wavelets and associated filterbanks for the analysis and representation of functions defined on circulant graphs. In this work, we leverage the inherent vanishing moment property of the circulant graph Laplacian…
Lagrangian coherent structures (LCS) in fluid flows appear as co-dimension one ridges of the finite time Lyapunov exponent (FTLE) field. In three- dimensions this means two-dimensional ridges. A fast algorithm is presented here to locate…
The current work reports the development of a new general grid generator called Gingred for arbitrary (e.g., number of X-points) 2D magnetic equilibria and plate geometries. A standardization of the construction of a grid is explained, the…
This work concerns with the following problem. Given a two-dimensional domain whose boundary is a closed polygonal line with internal boundaries defined also by polygonal lines, it is required to generate a grid consisting only of…
A grid-overlay finite difference method is proposed for the numerical approximation of the fractional Laplacian on arbitrary bounded domains. The method uses an unstructured simplicial mesh and an overlay uniform grid for the underlying…
We present a new meshless method for scalar diffusion equations which is motivated by their compatible discretizations on primal-dual grids. Unlike the latter though, our approach is truly meshless because it only requires the graph of…
Finite volume schemes for hyperbolic conservation laws require a numerical intercell flux. In one spatial dimension the numerical flux can be successfully obtained by solving (exactly or approximately) Riemann problems that are introduced…
We consider geometric multigrid methods for the solution of linear systems arising from isogeometric discretizations of elliptic partial differential equations. For classical finite elements, such methods are well known to be fast solvers…
This article presents a novel resolution to the problem of spline interpolation versus least-squares fitting on smooth Riemannian manifolds utilizing the method of gradient flows of networks. This approach represents a contribution to both…
Implicit neural networks have emerged as a crucial technology in 3D surface reconstruction. To reconstruct continuous surfaces from discrete point clouds, encoding the input points into regular grid features (plane or volume) has been…
This paper provides a construction method of the nearest graph Laplacian to a matrix identified from measurement data of graph Laplacian dynamics that include biochemical systems, synchronization systems, and multi-agent systems. We…