Neural operators, as a powerful approximation to the non-linear operators between infinite-dimensional function spaces, have proved to be promising in accelerating the solution of partial differential ...

Solver for coupled nonlinear partial differential equations (elliptic-parabolic conservation laws) based on the Voronoi finite volume method. It uses automatic differentiation via ForwardDiff.jl and ...

Adequate mathematical modeling is the key to success for many real-world projects in engineering, medicine, and other applied areas. Once a well-suited model is established, it can be thoroughly ...

Abstract: Many problems in science and engineering can be mathematically modeled using partial differential equations (PDEs), which are essential for fields like computational fluid dynamics (CFD), ...

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When the federal government shuts its doors, Americans get a glimpse at a long-debated question in Washington: How much government is too much? Here's what happens during a partial government shutdown ...

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Electromagnetic waves help to solve partial differential equations at the speed of light. Credit: R.G. MacDonald, A. Yakovlev, and V. Pacheco-Peña, doi 10.1117/1.APN.3.5.056007 In the domains of ...

Learn how to classify PDEs,and apply and visualize characteristic and finite difference solution methods. You can use these live scripts as demonstrations in lectures, class activities, or interactive ...