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Publication

RBF Based CWENO Method

Jan Sickmann Hesthaven, Fabian Mönkeberg
2020
Conference Papers

Abstract

Solving hyperbolic conservation laws on general grids can be important to reduce the computational complexity and increase accuracy in many applications. However, the use of non-uniform grids can introduce challenges when using high-order methods. We propose to use a Central WENO (CWENO) scheme based on radial basis function (RBF) interpolation, which is applicable to scattered data. We develop a smoothness indicator, based on RBFs, and CWENO specific weights which depend on the mesh size of the grid to construct an arbitrarily high order RBF-CWENO method. We evaluate the method with multiple examples in one dimension.

Official source

https://infoscience.epfl.ch/entities/publication/7d9119ee-36f3-4523-a9cd-79327b9053bb

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Jan Sickmann Hesthaven, Fabian Mönkeberg
2020
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/7d9119ee-36f3-4523-a9cd-79327b9053bb

About this result

Related concepts (22)

Euler method

In mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who first proposed it in his book Institutionum calculi integralis (published 1768–1870).

Iterative method

In computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones. A specific implementation with termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of the iterative method.

Computational complexity

In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations) and memory storage requirements. The complexity of a problem is the complexity of the best algorithms that allow solving the problem. The study of the complexity of explicitly given algorithms is called analysis of algorithms, while the study of the complexity of problems is called computational complexity theory.

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