Zobrazeno 1 - 10
of 24
pro vyhledávání: '"Fryklund, Fredrik"'
Over the last two decades, several fast, robust, and high-order accurate methods have been developed for solving the Poisson equation in complicated geometry using potential theory. In this approach, rather than discretizing the partial differential
Externí odkaz:
http://arxiv.org/abs/2409.11998
Autor:
Fryklund, Fredrik, Greengard, Leslie
We describe a new, adaptive solver for the two-dimensional Poisson equation in complicated geometries. Using classical potential theory, we represent the solution as the sum of a volume potential and a double layer potential. Rather than evaluating t
Externí odkaz:
http://arxiv.org/abs/2211.14537
A new scheme is proposed to construct an n-times differentiable function extension of an n-times differentiable function defined on a smooth domain D in d-dimensions. The extension scheme relies on an explicit formula consisting of a linear combinati
Externí odkaz:
http://arxiv.org/abs/2206.11318
Boundary integral methods are attractive for solving homogeneous linear constant coefficient elliptic partial differential equations on complex geometries, since they can offer accurate solutions with a computational cost that is linear or close to l
Externí odkaz:
http://arxiv.org/abs/2206.08825
Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular layer potentials in two dimensions. However, it can fail completely for the layer potentials belongi
Externí odkaz:
http://arxiv.org/abs/2108.00372
Integral equation based numerical methods are directly applicable to homogeneous elliptic PDEs, and offer the ability to solve these with high accuracy and speed on complex domains. In this paper, extensions to problems with inhomogeneous source term
Externí odkaz:
http://arxiv.org/abs/1907.08537
Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular layer potentials in two dimensions. However, it can fail completely for the layer potentials belongi
Externí odkaz:
http://arxiv.org/abs/1906.07713
Publikováno v:
In Journal of Computational Physics 15 February 2023 475
We introduce an efficient algorithm, called partition of unity extension or PUX, to construct an extension of desired regularity of a function given on a complex multiply connected domain in $2D$. Function extension plays a fundamental role in extend
Externí odkaz:
http://arxiv.org/abs/1712.08461
Publikováno v:
In Journal of Computational Physics 15 December 2018 375:57-79