We define higher-order analogues to the piecewise linear surface finite element method studied in [G. Dziuk, "Finite elements for the Beltrami operator on arbitrary surfaces," in Partial Differential ...

SIAM Journal on Numerical Analysis, Vol. 50, No. 6 (2012), pp. 3351-3374 (24 pages) In this paper quasi-Monte Carlo (QMC) methods are applied to a class of elliptic partial differential equations ...

Abstract: In this work, a finite element method (FEM)-based numerical framework is proposed to effectively calculate the drift-diffusion equations and compiled into a parallel computing device ...

Abstract: Current forward modeling approaches for 3-D controlled-source electromagnetic (CSEM) problems in anisotropic media exhibit limited capability in addressing large-scale models. Given that, we ...

Companies all over the world are using AI to identify rare earth minerals, reducing the need to drill unnecessarily in the exploration phase.

This repository is my implementation of: "Can Physics-Informed Neural Networks beat the Finite Element Method? by Tamara G. Grossmann, Urszula Julia Komorowska, Jonas Latz and Carola-Bibiane Schönlieb ...

Spintronics devices will be key to realizing faster and more energy-efficient computers. To give us a better understanding of ...

By extending a proof of a physically important behavior in one-dimensional quantum spin systems to higher dimensions, a RIKEN ...

Discover how first principles thinking can solve complex problems, drive innovation, and transform your approach to ...