mkBCint2 - Create the core of the solver for mixed elements
Calling sequence:
mkBCint2(eq_list, unknown_list, old_unknown_list, params_list, unkntestlist, testbsflist);
Parameters:
eq_list - A list of equations defining a PDE problem in variational form.
unknown_list - The list of unknowns as discussed above.
old_unknown_list - The list of unknowns at the previous timestep, as discussed above.
params_list - A list of scalar input parameters.
unkntestlist - A list of testfunction names that couple a certain testfunction with a certain unknown. The number of entries in unkntestlist must be the same as in unknown_list and old_unknown_list.
testbsflist - A list containing three entries, the first two being names of testfunctions, the last the name of a file that contins the definitions of the basefunctions. The two basefunction names are identified with the actual basefunctions via ordering and the name of this file, i.e., with testbsflist:=[v(x,y),q(x,y),`2DP2P1_gsq_bsf`], v(x,y) is P2 and q(x,y) is P1.
Synopsis:
ElementInt(expr)
These are ignored in mkBCint2.
ElementIntHiQ(expr)
These are ignored in mkBCint2.
BoundaryInt(expr)
The BoundaryInt call is used to evaluate the boundary integrals that appear in natural boundary conditions in variational formulations. BoundaryInt generates local residuals by integration over element sides. These are assembled for sides located on parts of the boundary that have 'Neumann' boundary conditions. If the string 'qBCval' is encountered it will be replaced by a number read with the mesh when the solver is run. The equations in eq_list must consist of terms enclosed in ElementInt or BoundaryInt calls, or the entire equation be enclosed in a CopyEq().
CopyEq(variable=expression)
Equations enclosed in CopyEq() are ignored by mkBCint.
NoExpand(expr)
This is meaningful only when used in the argument of an ElementInt or BoundaryInt function. It alters the way the symbolic calculations are done, but should not affect the numerical results. It can be used to prevent Maple from expanding nonlinear expressions of variables into huge, awkward expressions. For example: BoundaryInt(test(x,y)*(NoExpand(u(x,y)) )^3) could produce less code than BoundaryInt(test(x,y)*(u(x,y))^3).
Lump2(expr)
This is an implementation of the familiar FEM-trick of 'lumping the mass matrix'.
PointWise(expr)
This is an implementation of a trick sometimes used in FEM, for cheaper evaluation of nonlinear expressions. It will apply a nonlinear expression to the nodal values directly, instead of first expanding the unknown in base functions, i.e.: u(x,y)^3 is expanded in base functions as sum_i( u_i^3 * test_i) instead of ( sum_i( ui * test_i))^3. PointWise() is meaningful only when used in the argument of an ElementInt or BoundaryInt function.
Examples:
> eq_list:= [nseq[1],nseq[2],pPoisseq,poldeq]:
> unknown_list:= [u[1](x,y),u[2](x,y),p(x,y),pdum(x,y)]:
> old_unknown_list:= [u0[1](x,y),u0[2](x,y),p0(x,y),p00(x,y)]:
> params_list:= [Reno,Pe,qqSDpar]:
> unkntestlist:=[v(x,y),v(x,y),q(x,y),q(x,y)]:
> testbsflist:=[v(x,y),q(x,y),`2DP2P1_gsq_bsf`]:
> size_parameters:=mkBCint2(eq_list, unknown_list,old_unknown_list,params_list,unkntestlist,testbsflist);
grbcrs
bdedsp
adbr1
adbm1
adbr2
adbm2