Better simulation meshes well for design software (and more)

Monday, July 20, 2020 - 14:30 in Mathematics & Economics

The digital age has spurred the rise of entire industries aimed at simulating our world and the objects in it. Simulation is what helps movies have realistic effects, automakers test cars virtually, and scientists analyze geophysical data. To simulate physical systems in 3D, researchers often program computers to divide objects into sets of smaller elements, a procedure known as “meshing.” Most meshing approaches tile 2D objects with patterns of triangles or quadrilaterals (quads), and tile 3D objects with patterns of triangular pyramids (tetrahedra) or bent cubes (hexahedra, or “hexes”). While much progress has been made in the fields of computational geometry and geometry processing, scientists surprisingly still don’t fully understand the math of stacking together cubes when they are allowed to bend or stretch a bit. Many questions remain about the patterns that can be formed by gluing cube-shaped elements together, which relates to an area of math called topology. New work out...

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