## 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 system of equations involving sparse matrices. There are therefore a number of application fields, among which we list in the following some of the ones cited by the users of our sparse direct solver Mumps (see Section 5.2 ): structural mechanical engineering (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 (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 (chemical process modeling), vibro-acoustics, aero-acoustics, aero-elasticity, optical fiber modal analysis, blast furnace modeling, glaciology (models 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 ( Mumps can for example be used on each subdomain in an iterative framework), circuit simulations, etc.