Computer graphics and geometry processing research provide the tools needed to simulate physical phenomena like fire and flames, aiding the creation of visual effects in video games and movies as well ...

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 ...

Studies properties and solutions of partial differential equations. Covers methods of characteristics, well-posedness, wave, heat and Laplace equations, Green's functions, and related integral ...

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Calculation: A representation of a network of electromagnetic waveguides (left) being used to solve Dirichlet boundary value problems. The coloured diagrams at right represent the normalized ...

This book serves as a bridge between graduate textbooks and research articles in the area of nonlinear elliptic partial differential equations. Whereas graduate textbooks present basic concepts, the ...

Two new approaches allow deep neural networks to solve entire families of partial differential equations, making it easier to model complicated systems and to do so orders of magnitude faster. In high ...

Luis Caffarelli has won the 2023 Abel prize, unofficially called the Nobel prize for mathematics, for his work on a class of equations that describe many real-world physical systems, from melting ice ...