natural frequencies of liquid sloshing in tanks. Boundary element method is one of the most effective methods for numerical simulation of contact problems, in particular for simulation of adhesive contacts. Boundary element formulations typically give rise to fully populated matrices. This means that the storage requirements and computational time will tend to grow according to the square of the problem size. By contrast, finite element matrices are typically banded (elements are only locally connected) and the storage requirements for the system matrices typically grow quite linearly with the problem size. Compression techniques (e.g. multipole expansions or adaptive cross approximation/hierarchical matrices) can be used to ameliorate these problems, though at the cost of added complexity and with a success-rate that depends heavily on the nature of the problem being solved and the geometry involved. See also Analytic element method Computational electromagnetics Meshfree methods Immersed boundary method Stretched grid method Modified radial integration method References Bibliography . . . , available also here. . . (in two volumes). Further reading External links An Online Resource for Boundary Elements What lies beneath the surface? A guide to the Boundary Element Method and Green's functions for the students and professionals An introductory BEM course (with a chapter on Green's functions) Boundary elements for plane crack problems Electromagnetic Modeling web site at Clemson University (includes list of currently available software) Concept Analyst Boundary Element Analysis software Klimpke, Bruce A Hybrid Magnetic Field Solver Using a Combined Finite Element/Boundary Element Field Solver, U.K. Magnetics Society Conference, 2003 which compares FEM and BEM methods as well as hybrid approaches Free software Bembel A 3D, isogeometric, higher-order, open-source BEM software for Laplace, Helmholtz and Maxwell problems utilizing a fast multipole method for compression and reduction of computational cost boundary-element-method.com An open-source BEM software for solving acoustics / Helmholtz and Laplace problems Puma-EM An open-source and high-performance Method of Moments / Multilevel Fast Multipole Method parallel program AcouSTO Acoustics Simulation TOol, a free and open-source parallel BEM solver for the Kirchhoff-Helmholtz Integral Equation (KHIE) FastBEM Free fast multipole boundary element programs for solving 2D/3D potential, elasticity, Stokes flow and acoustic problems ParaFEM Includes the free and open-source parallel BEM solver for elasticity problems described in Gernot Beer, Ian Smith, Christian Duenser, The Boundary Element Method with Programming: For Engineers and Scientists, Springer, (2008) Boundary Element Template Library (BETL) A general purpose C++ software library for the discretisation of boundary