Computer graphics and geometry processing research provide the tools needed to simulate physical phenomena like fire and ...

In fields such as physics and engineering, partial differential equations (PDEs) are used to model complex physical processes to generate insight into how some of the most complicated physical and ...

Mathematical approaches for numerically solving partial differential equations. The focus will be (a) iterative solution methods for linear and non-linear equations, (b) spatial discretization and ...

Linear and quasilinear first order PDE. The method of characteristics. Conservation laws and propagation of shocks. Basic theory for three classical equations of mathematical physics (in all spatial ...

Finite element methods (FEM) constitute a foundational numerical approach for solving partial differential equations by discretising complex domains into smaller, manageable subdomains known as ...

This work proposes and analyzes a stochastic collocation method for solving elliptic partial differential equations with random coefficients and forcing terms. These input data are assumed to depend ...

Developing algorithms for solving high-dimensional partial differential equations (PDEs) has been an exceedingly difficult task for a long time, due to the notoriously difficult problem known as the ...

FlexPDE 5 is a script-driven program for solving partial differential equations involving heat flow, electric and magnetic fields, and stress analysis. Users enter equations, boundary conditions, ...

The researchers’ device applies principles of neural networking to an optical framework. As a wave encoded with a PDE passes through the ONE’s series of components, its properties gradually shift and ...