The mGFD (meshless Generalized Finite Differences) repository provides a comprehensive solution for numerically solving Partial Differential Equations in two dimensions on highly irregular regions.
Compared to the conventional high-order staggered-grid finite-difference method (C-SFD), the time–space domain dispersion-relation-based high-order staggered-grid finite-difference method (TS-SFD) can ...
ABSTRACT: The solution of the Riemann Problem (RP) for the one-dimensional (1D) non-linear Shallow Water Equations (SWEs) is known to produce four potential wave patterns for the scenario where the ...
Abstract: This letter proposes a generalized and controllable-stability conformal method to address stability challenges inherent in conformal finite-difference time-domain algorithms. A quantitative ...
Creative Commons (CC): This is a Creative Commons license. Attribution (BY): Credit must be given to the creator. The development of machine learning interatomic potentials (MLIPs) has revolutionized ...
Abstract: In this letter, a 2-D parameter-optimized spatial finite-difference temporal differential (SFDTD) method is presented, referred to as the PO-SFDTD method. First, the dispersion ...
A new approach in the finite difference framework is developed, which consists of three steps: choosing the dimension of the local approximation subspace, constructing a vector basis for this subspace ...
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