Parallel ABS projection methods for linear and nonlinear systems with block arrowhead structure

We investigate the implementation of the block implicit LU 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 Schmidt and Hoyer [1], the basic corrected implicit method of Zhang et al. [2], and the capacitance matrix method of Bjørstad and Widlund [3], as special cases. Experimental results which indicate the usefulness of the method are also mentioned. © 1999 Elsevier Science Ltd. All rights reserved.