## Section: Application Domains

### Applications of Sparse Direct Solvers

In the context of our activity on sparse direct (multifrontal) solvers in distributed environments, we develop, distribute, maintain and support competitive software. Our methods have a wide range of applications, and they are at the heart of many numerical methods in simulation: whether a model uses finite elements or finite differences, or requires the optimization of a complex linear or nonlinear function, one almost always ends up solving a linear system of equations involving sparse matrices. There are therefore a number of application fields, among which we list some cited by the users of our sparse direct solver Mumps (see Section 5.2 ): structural mechanical engineering (e.g., stress analysis, structural optimization, car bodies, ships, crankshaft segment, offshore platforms, computer assisted design, computer assisted engineering, rigidity of sphere packings); heat transfer analysis; thermomechanics in casting simulation; fracture mechanics; biomechanics; medical image processing; tomography; plasma physics (e.g., Maxwell's equations), critical physical phenomena, geophysics (e.g., seismic wave propagation, earthquake related problems); ad-hoc networking modeling (e.g., Markovian processes); modeling of the magnetic field inside machines; econometric models; soil-structure interaction problems; oil reservoir simulation; computational fluid dynamics (e.g., Navier-Stokes, ocean/atmospheric modeling with mixed finite elements methods, fluvial hydrodynamics, viscoelastic flows); electromagnetics; magneto-hydro-dynamics; modeling the structure of the optic nerve head and of cancellous bone; modeling of the heart valve; modeling and simulation of crystal growth processes; chemistry (e.g., chemical process modeling); vibro-acoustics; aero-acoustics; aero-elasticity; optical fiber modal analysis; blast furnace modeling; glaciology (e.g., modeling of ice flow); optimization; optimal control theory; astrophysics (e.g., supernova, thermonuclear reaction networks, neutron diffusion equation, quantum chaos, quantum transport); research on domain decomposition (e.g., Mumps is used on subdomains in an iterative solver framework); and circuit simulations.