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鲲鹏小智

可替换性

MKL中包含单机版直接求解器PARDISO（Parallel Direct Sparse Solver Interface）和集群版直接求解器PARDISO-Cluster（Parallel Direct Sparse Solver for Cluster Interface）。前者为shared-memory版本的并行稀疏求解器，而后者则和SCADSS一样，支持MPI和OPENMP技术的混合模式。直接求解器包含Analyze，Factorize，Solve三个核心阶段，每个阶段都可以单独调用。这一点与用户的实际问题相关，比如用户在求解部分包含时间项的偏微分方程的时候，系数矩阵是保持不变的，因此Analyze和Factorize只需要进行一次，重复调用Solve阶段即可。再比如，系数矩阵的数值发生了变化，但是矩阵的非零元位置未发生变化，那么Analyze只需要进行一次，重复调用Solve阶段即可。在这里给出MKL中的direct solver与SCADSS的接口映射关系。

表1 PARDISO-Cluster与SCADSS的替换映射关系

PARDISO-Cluster接口

SCADSS接口

mtype=2;或者mtype = 4;

phase = 11;

cluster_sparse_solver(pt, &maxfct, &mnum, &mtype, &phase, &n, a, ia, ja, &perm, &nrhs, iparm, &msglvl, b, x, &comm, &error);

KmlScadssSpdAnalyzeDI(&handle);或者

KmlScadssHpdAnalyzeDI(&handle);

mtype=2;或者mtype = 4;

phase = 22;

cluster_sparse_solver(pt, &maxfct, &mnum, &mtype, &phase, &n, a, ia, ja, &perm, &nrhs, iparm, &msglvl, b, x, &comm, &error);

KmlScadssSpdFactorizeDI(&handle);或者

KmlScadssSpdFactorizeDI(&handle);

mtype=2;或者mtype = 4;

phase = 33;

cluster_sparse_solver(pt, &maxfct, &mnum, &mtype, &phase, &n, a, ia, ja, &perm, &nrhs, iparm, &msglvl, b, x, &comm, &error);

KmlScadssSpdSolveDI(&handle);或者

KmlScadssSpdSolveDI(&handle);

mtype=2;或者mtype = 4;

phase = -1;

cluster_sparse_solver(pt, &maxfct, &mnum, &mtype, &phase, &n, a, ia, ja, &perm, &nrhs, iparm, &msglvl, b, x, &comm, &error);

KmlScadssSpdCleanDI(&handle);或者

KmlScadssSpdCleanDI(&handle);
  1. MKL中direct solver通过mtype参数确定输入稀疏矩阵的类型，mtype=2表示SPD矩阵，mtype=4则表示HPD矩阵。
  2. phase参数控制MKL direct solver执行的操作，除上表中列举的取值外，还可以取别的值。例如取12时表示执行Analyze，Factorize两个过程。
表2 PARDISO与SCADSS的替换映射关系

PARDISO接口

SCADSS接口

mtype=2;或者mtype = 4;

phase = 11;

pardiso(pt, &maxfct, &mnum, &mtype, &phase, &n, a, ia, ja, &perm, &nrhs, iparm, &msglvl, b, x, &error);

KmlScadssSpdAnalyzeDI(&handle);或者

KmlScadssHpdAnalyzeDI(&handle);

mtype=2;或者mtype = 4;

phase = 22;

pardiso(pt, &maxfct, &mnum, &mtype, &phase, &n, a, ia, ja, &perm, &nrhs, iparm, &msglvl, b, x, &error);

KmlScadssSpdFactorizeDI(&handle);或者

KmlScadssHpdFactorizeDI(&handle);

mtype=2;或者mtype = 4;

phase = 33;

pardiso(pt, &maxfct, &mnum, &mtype, &phase, &n, a, ia, ja, &perm, &nrhs, iparm, &msglvl, b, x, &error);

KmlScadssSpdSolveDI(&handle);或者

KmlScadssHpdSolveDI(&handle);

mtype=2;或者mtype = 4;

phase = -1;

pardiso(pt, &maxfct, &mnum, &mtype, &phase, &n, a, ia, ja, &perm, &nrhs, iparm, &msglvl, b, x, &error);

KmlScadssSpdCleanDI(&handle);或者

KmlScadssHpdCleanDI(&handle);