k*********g
发帖数: 791 | 1 canonical definitions of galerkin methods and collocations methods.
the definition of galerkin methods vary in different communities of
scientific computing.
since spectral-based methods will be the future of numerical computation for
continuum, the canonical definition of galerkin sort of follows the bible "
C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang. Spectral Methods,
Fundamentals in Single Domains. Springer-Verlag, 2006":
if the core computation is conducted in the transformed space (wave number
space) in a best-fitting manner, then it is named as galerkin method.
in contrast, if the core computation is conducted in the physical space in
an exact-fitting manner, then it is named as collocation method.
以下就是搞这些“迂腐、学究式”的定义的直接benefit：
根据排列组合，2 types of spectral based methods are missing:
transformed space + exact fitting, which seemingly to be pointless
and
physical space + best fitting, which turns out extremely powerful. | k*********g
发帖数: 791 | | j****x
发帖数: 943 | 3 As to the definition of galerkin and collocation method, in general, shouldn
't that be: collocation=exact fitting on nodes and galerkin=best fitting, i.
e. minimum of residual? | c***r
发帖数: 1570 | 4 手上正好还有这本书，再翻了翻。
collocation没有那么神话，在我看来就是基于chebyshev + gauss /gauss-lobatto的
高阶有限差分而已。此外，collocation方法出来的stiffness matrix永远是非对称的
，增加求解难度和时间。collocation 做multi-domain就是灾难。collocation做
hyperbolic,parabolic也是灾难。 | k*********g
发帖数: 791 | 5 不对称矩阵。。。。
你还是停留在学习2、3流研究者写的书的层次上。。。
看看这个吧：
http://www.mitbbs.com/article_t/Computation/31164387.html
【在 c***r 的大作中提到】
: 手上正好还有这本书，再翻了翻。
: collocation没有那么神话，在我看来就是基于chebyshev + gauss /gauss-lobatto的
: 高阶有限差分而已。此外，collocation方法出来的stiffness matrix永远是非对称的
: ，增加求解难度和时间。collocation 做multi-domain就是灾难。collocation做
: hyperbolic,parabolic也是灾难。
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