solve(u) begin onbdy()...; onbdy()...; ...; pde(u)... end;
For 2-systems and the use of solve(u,v)
, see the section 2-Systems
.
It defines a PDE and its boundary conditions.
It will be solved by the Finite Element Method of degree 1 on triangles
and a Gauss factorization.
Once the matrix is built and factorized solve
may be called again by
solve(u,-1)...;
then the matrix is not rebuilt nor factorized and
only a solution of the linear system is performed by an up and a down
sweep in the Gauss algorithm only. This saves a lot of CPU time whenever
possible. Several matrices can be stored and used simultaneously, in
which case the sequence is
solve(u,i)...; ... solve(u,-i)...;where
i
is a scalar variable (not an array function).
However matrices must be constructed in the natural order: i=1
first
then i=2....
after they can be re-used in any order. One can also
re-use an old matrix with a new definition, as in
solve(u,i)...; ... solve(u,i)...; solve(u,ħi)...;Notice that
solve(u)
is equivalent to solve(u,1)
.
Remark: 2-Systems have their own matrices, so they do not count in the previous ordering.