GPU Preconditioning for Block Linear Systems Using Block Incomplete Sparse Approximate Inverses
Algorithm 1
Block-ISAI preconditioning on GPU: .
Input:
(1) The BILU triangular factors, L and U;
(2) Input vector, ;
Output:
(1) The preconditioned vector, ;
S1: setup step:
S1.1: estimate the sparsity patterns for the inverses of L and U expressed as NL and NU: and ;
S1.2: extract and from L and U, where and are the non-zero patterns at the column of NL and NU, respectively, indexing block rows and columns in L to form and indexing block rows and columns in U to form ;
S1.3: form two groups of small block triangular systems in (7), LGSBTS: and UGSBTS: , by looping overall and ;
S1.4: solve LGSBTS and UGSBTS for the solutions of NL and NU: solve block lower and upper triangular systems in (7) in parallel.
