矩阵分解成若干块求解

xsxcn

对于Ax=b, A的size很大,能不能把A分解成几块来并行求解？有没有这方面的资料？

caoer

many schemes about block matrix method, mainly focusing on the multiplication.
but it isnt impossible to find a block matrix method for linear algebra.
For parallel solver, it is not just simple blocked matrix. many tricks there.
after all, the setup for ghost node or halo is not trivial.

the solution is , I recommend, you better off use the matured opensource library
instead of starting everything from the scratch. The candidate packages are PETSc, umfpack,
superlu, etc.

penultimate

分块LDLT求解的方法很成熟，目前有钟万勰的单块缓冲和SAP的多块缓冲法，具体就要参看相关的资料了。
并行求解对于LDLT分解很复杂，也可以作，多个主块的分解作为块内和块外过程分解时，就可以部分解耦，实现有条件并行分解。
如果用迭代求解的话，有很多并行的算法可用，还可以利用GPU的浮点数运算功能，效果提升显著