Meshing and Simulation

Design meshes are  a means for determining the design of simulation, especially for design problems.  Good discussion.

Better simulation meshes well for design software (and more)
New work on 2D and 3D meshing aims to address challenges with some of today’s state-of-the-art methods.   By Adam Conner-Simons | MIT CSAIL

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 of MIT’s Computer Science and Artificial Intelligence Laboratory (CSAIL) aims to explore several of these questions. Researchers have published a series of papers that address shortcomings of existing meshing tools by seeking out mathematical structure in the problem. In collaboration with scientists at the University of Bern and the University of Texas at Austin, their work shows how areas of math like algebraic geometry, topology, and differential geometry could improve physical simulations used in computer-aided design (CAD), architecture, gaming, and other sectors.

“Simulation tools that are being deployed ‘in the wild’ don’t always fail gracefully,” says MIT Associate Professor Justin Solomon, senior author on the three new meshing-related papers. “If one thing is wrong with the mesh, the simulation might not agree with real-world physics, and you might have to throw the whole thing out.”  .... ' 

In one paper,  https://diglib.eg.org/handle/10.1111/c 4074a gf14074a team led by MIT undergraduate Zoë Marschner developed an algorithm to repair issues that can often trip up existing approaches for hex meshing, specifically.  ..."