Parallel ABS projection methods for linear and nonlinear systems with block arrowhead structure. (English) Zbl 0945.65056
Summary: We investigate the implementation of the block implicit LU Abaffy-Broyden-Spedicato (ABS) methods on linear and nonlinear algebraic systems with block arrowhead coefficient or Jacobian matrix. Connections with other methods specialized for such problems are investigated in detail. It is shown that the block implicit LU ABS method contains method 2 of W. Hoyer and J. W. Schmidt [Z. Angew. Math. Mech. 64, 397-405 (1984; Zbl 0567.65028)], the basic corrected implicit method of X. Zhang, R. H. Byrd and R. B. Schnabel [SIAM J. Sci. Stat. Comput. 13, No. 4, 841-859 (1992; Zbl 0757.65064)], and the capacitance matrix method of P. E. Bjørstad and O. B. Widlund [SIAM J. Numer. Anal. 23, 1097-1120 (1986; Zbl 0615.65113)], as special cases. Experimental results which indicate the usefulness of the method are also mentioned.
MSC:
| 65H10 | Numerical computation of solutions to systems of equations |
| 65F05 | Direct numerical methods for linear systems and matrix inversion |
Keywords:
block implicit LU factorization; parallel computation; comparison of methods; structured sparsity; Abaffy-Broyden-Spedicato methods; linear and nonlinear algebraic systems; ABS method; capacitance matrix methodReferences:
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