d****a
发帖数: 23 | 1 It is an 3D elliptic problem with periodic boundary conditions in lateral
boundaries and fixed top and bottom boundary condtions. After discretizing
by finite difference method, I get a big coefficient matrix with 39 nonzero
elements in each row. The matrix has dimension about 75,0000. Now the
problem is to solve the sparse linear system. However, this matrix elements
have a large numerical range, spaning 10 orders of magnitude. It is
nonsymmetric, not diagonally dominant, and not positive defin | b***e
发帖数: 38 | 2 Perhaps you need to go back to physics or work on basis functions to make
the matrix better conditioned.
nonzero
elements
Sparse
【在 d****a 的大作中提到】
: It is an 3D elliptic problem with periodic boundary conditions in lateral
: boundaries and fixed top and bottom boundary condtions. After discretizing
: by finite difference method, I get a big coefficient matrix with 39 nonzero
: elements in each row. The matrix has dimension about 75,0000. Now the
: problem is to solve the sparse linear system. However, this matrix elements
: have a large numerical range, spaning 10 orders of magnitude. It is
: nonsymmetric, not diagonally dominant, and not positive defin
| s**i
发帖数: 381 | 3 exactly.
Try to make it s.p.d
Or maybe implicit scheme is not a good idea for this problem at all.
【在 b***e 的大作中提到】
: Perhaps you need to go back to physics or work on basis functions to make
: the matrix better conditioned.
:
: nonzero
: elements
: Sparse
| d****a
发帖数: 23 | 4 Thank you guys for the input.
I can make the matrix better scaled such that the numerical range falling
into 2 orders of magnitude. Actually it is a fluid mechanic problem seeking
for the steady state internal wave solutions. My solver gives solutions for
some idealized cases, like giving a constant flow field. If the flow is zero
, it become simply a 3D Laplace problem, which is easy to solve.
Talking about make it symmetric, positive definitive ...
The wave operator itself was actually singula
【在 s**i 的大作中提到】
: exactly.
: Try to make it s.p.d
: Or maybe implicit scheme is not a good idea for this problem at all.
| b***e
发帖数: 38 | 5 Here are my 2 cents although I am not working on fluid mechnics.
On the numerical side, try preconditioned GMRES if Gaussian elimination with
pivoting does not fail.
If the previous does not work, check out whether the system of equations is
diagonalizable.
Finally, if this is an eigenvalue problem, try to solve it as an eigenvalue
problem.
good luck.
seeking
for
zero
【在 d****a 的大作中提到】
: Thank you guys for the input.
: I can make the matrix better scaled such that the numerical range falling
: into 2 orders of magnitude. Actually it is a fluid mechanic problem seeking
: for the steady state internal wave solutions. My solver gives solutions for
: some idealized cases, like giving a constant flow field. If the flow is zero
: , it become simply a 3D Laplace problem, which is easy to solve.
: Talking about make it symmetric, positive definitive ...
: The wave operator itself was actually singula
|
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