Abstract
Boundary value problems related to elliptic partial differential equations are belonging to a class of computing-intensive applications. A significant portion of real problems solved on advanced supercomputers has its origin in approximation of equations of this type. A main feature which characterizes numerical solving these problems is concerned with large linear algebraic systems with sparse matrices which put requirements on computer speed and memory capacity, when practically usable results are expected. Among them, the Poisson and biharmonic equations play a key role in such areas as aerodynamics, electronics, mechanics and civil engineering. Both equations represent also basic blocks needed to be solved in inner loops for more complicated nonlinear problems. The underlying operator in these problems is the discretized Laplacian. For these equation with a single operator, a number of fast sequential and parallel algorithms has been developed [3], [6], [12],[10].
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Vajteršic, M. (1997). VLSI Solvers for Some PDE Problems. In: Grandinetti, L., Kowalik, J., Vajtersic, M. (eds) Advances in High Performance Computing. NATO ASI Series, vol 30. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5514-4_7
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DOI: https://doi.org/10.1007/978-94-011-5514-4_7
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