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Parallel implicit-explicit general linear methods
High-order discretizations of partial differential equations (PDEs) nece...
02/03/2020 ∙ by Steven Roberts, et al. ∙
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A machine learning solver for high-dimensional integrals: Solving Kolmogorov PDEs by stochastic weighted minimization and stochastic gradient descent through a high-order weak
The paper introduces a very simple and fast computation method for high-...
12/22/2020 ∙ by Riu Naito, et al. ∙
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A single-step third-order temporal discretization with Jacobian-free and Hessian-free formulations for finite difference methods
Discrete updates of numerical partial differential equations (PDEs) rely...
05/29/2020 ∙ by Youngjun Lee, et al. ∙
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Explicit high-order energy-preserving methods for general Hamiltonian partial differential equations
A novel class of explicit high-order energy-preserving methods are propo...
01/03/2020 ∙ by Chaolong Jiang, et al. ∙
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High-order curvilinear mesh in the numerical solution of PDEs with moving frames on the sphere
When time-dependent partial differential equations (PDEs) are solved num...
08/23/2019 ∙ by Sehun Chun, et al. ∙
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Hyperviscosity-Based Stabilization for Radial Basis Function-Finite Difference (RBF-FD) Discretizations of Advection-Diffusion Equations
We present a novel hyperviscosity formulation for stabilizing RBF-FD dis...
06/11/2018 ∙ by Varun Shankar, et al. ∙
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An Efficient High-Order Meshless Method for Advection-Diffusion Equations on Time-Varying Irregular Domains
We present a high-order radial basis function finite difference (RBF-FD)...
11/13/2020 ∙ by Varun Shankar, et al. ∙
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High-order maximum-entropy collocation methods
10/26/2020 ∙ by F. Greco, et al. ∙
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This paper considers the approximation of partial differential equations with a point collocation framework based on high-order local maximum-entropy schemes (HOLMES). In this approach, smooth basis functions are computed through an optimization procedure and the strong form of the problem is directly imposed at the collocation points, reducing significantly the computational times with respect to the Galerkin formulation. Furthermore, such a method is truly meshless, since no background integration grids are necessary. The validity of the proposed methodology is verified with supportive numerical examples, where the expected convergence rates are obtained. This includes the approximation of PDEs on domains bounded by implicit and explicit (NURBS) curves, illustrating a direct integration between the geometric modeling and the numerical analysis.
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