Abstract
The solution of new classes of application problems in the fields of continuum mechanics, including the problems of three-dimensional aerodynamics and hydrodynamics, space physics, and environmental science often require considerable computer resources which are often too great even for the leading and best equipped research centers. We believe this problem can be solved by employing up-to-date methods based on irregular adapting grids. For the solution of two-dimensional elliptic problems an adaptive projection-grid method has been designed. The solution is sought as a piecewise-polynomial function. Overdetermined system collocation equations of the differential equation and special mixed conform conditions are used for defining of the coefficients of these polynomials. It is sought on a sequence of grids adapted to the singularities of the solution and to the domain geometry, see also Shokin, Sleptsov (1995) and Sleptsov, Shokin (1995).
Comprehensive grid generation method which enables the user to generate both adaptive and fixed grids in a unified manner on surfaces and in domains was developed. Namely the adaptive grid in the domain is formed as the projection of the uniform grid from a monitor surface. The method relies on a variational approach of generating uniform grids on hypersurfaces, see Liseikin (1991).
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Shokin, Y.I. (1997). New resource-sparing grid methods for solving the problems of mathematical physics. In: Boisvert, R.F. (eds) Quality of Numerical Software. IFIP Advances in Information and Communication Technology. Springer, Boston, MA. https://doi.org/10.1007/978-1-5041-2940-4_32
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DOI: https://doi.org/10.1007/978-1-5041-2940-4_32
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