Engineer here with a lot of experience with Finite Element Analysis software. Sparse arrays are NOT some amusing construct to see how well you code an obscure problem. FEA is *THE* tool to create a design that is less likely to fail. Programs such as ANSYS are used design just about every single vehicle on the road (cars, trucks, bicycles), airplanes -- the airframe and the engines, locomotives. And FEA is also used to design bridges, buildings, cranes used to build this stuff. The use of sparse matrix algorithms enable this software to get results in a reasonable time frame. As mentioned elsewhere, sparse matrices are very useful in design optimization, which is frequently coupled with FEA.