Search results for "Mathematics::Numerical Analysis"
showing 7 items of 57 documents
WENO schemes applied to the quasi-relativistic Vlasov-Maxwell model for laser-plasma interaction
2014
Abstract In this paper we focus on WENO-based methods for the simulation of the 1D Quasi-Relativistic Vlasov–Maxwell (QRVM) model used to describe how a laser wave interacts with and heats a plasma by penetrating into it. We propose several non-oscillatory methods based on either Runge–Kutta (explicit) or Time-Splitting (implicit) time discretizations. We then show preliminary numerical experiments.
Non-periodic Discrete Splines
2015
Discrete Splines with different spans were introduced in Sect. 3.3.1. This chapter focuses on a special case of discrete splines whose spans are powers of 2. These splines are discussed in more detail. The Zak transform provides an integral representation of such splines. Discrete exponential splines are introduced. Generators of the discrete-spline spaces are described whose properties are similar to properties of polynomial-spline spaces generators. Interpolating discrete splines provide efficient tools for upsampling 1D and 2D signals. An algorithm for explicit computation of discrete splines is described.
Some Theoretical Results About Stability for IMEX Schemes Applied to Hyperbolic Equations with Stiff Reaction Terms
2010
In this work we are concerned with certain numerical difficulties associated to the use of high order Implicit–Explicit Runge–Kutta (IMEX-RK) schemes in a direct discretization of balance laws with stiff source terms. We consider a simple model problem, introduced by LeVeque and Yee in [J. Comput. Phys 86 (1990)], as the basic test case to explore the ability of IMEX-RK schemes to produce and maintain non-oscillatory reaction fronts.
Polynomial Spline-Wavelets
2015
This chapter presents wavelets in the spaces of polynomial splines. The wavelets’ design is based on the Zak transform, which provides an integral representation of spline-wavelets. The exponential wavelets which participate in the integral representation are counterparts of the exponential splines that were introduced in Chap. 4. Fast algorithms for the wavelet transforms of splines are presented. Generators of spline-wavelet spaces are described, such as the B-wavelets and their duals and the Battle-Lemarie wavelets whose shifts form orthonormal bases of the spline-wavelet spaces.
Quadrature domains for the Helmholtz equation with applications to non-scattering phenomena
2022
In this paper, we introduce quadrature domains for the Helmholtz equation. We show existence results for such domains and implement the so-called partial balayage procedure. We also give an application to inverse scattering problems, and show that there are non-scattering domains for the Helmholtz equation at any positive frequency that have inward cusps.
Functional a posteriori error estimates for boundary element methods
2019
Functional error estimates are well-established tools for a posteriori error estimation and related adaptive mesh-refinement for the finite element method (FEM). The present work proposes a first functional error estimate for the boundary element method (BEM). One key feature is that the derived error estimates are independent of the BEM discretization and provide guaranteed lower and upper bounds for the unknown error. In particular, our analysis covers Galerkin BEM and the collocation method, what makes the approach of particular interest for scientific computations and engineering applications. Numerical experiments for the Laplace problem confirm the theoretical results.
Reverse Catmull-Clark Subdivision
2006
Reverse subdivision consists in constructing a coarse mesh of a model from a finer mesh of this same model. In this paper, we give formulas for reverse Catmull-Clark subdivision. These formulas allow the constructing of a coarse mesh for almost all meshes. The condition for being able to apply these formulas is that the mesh to be reversed must be generated by the subdivision of a coarse mesh. Except for this condition, the mesh can be arbitrary. Vertices can be regular or extraordinary and the mesh itself can be arbitrary (triangular, quadrilateral…).