test_subs

test_subs - Generate equations from variational forms

Calling sequence:

test_subs(test_list,testfcn,expr)

Parameters

test_list - a list of test functions

test_fcn - a name of a variable to be used as a test function

expr - An expression.

Synopsis:

When deriving FEM formulations for systems of PDEs, it may be convenient to multiply each equation by a different test function, and add them together to one large integral form. To recover the individual equations in a form suitable for input to for example mkFem, all test functions except one are replaced by 0. test_subs provides a convenient shorthand for this.
test_list is a list of the names of the different formal test functions.
testfcn is a name of a test function to be used with for example mkFem.
The output is a list of equations in a form suitable for input to mkFem.

Examples:

> ueq:=0=diff(u(x),x,x); 2 d ueq := 0 = --- u(x) 2 dx > veq:=u(x)=diff(v(x),x,x); 2 d veq := u(x) = --- v(x) 2 dx > varForm:=ElementInt(ut(x) * (lhs(ueq)-rhs(ueq)))+ ElementInt(vt(x) * (lhs(veq)-rhs(veq))) =0: > pivarForm:=partInt(varForm,[u(x),v(x)]): > BCpivarForm:=BCsubs([diff(u(x),x)=q,diff(v(x),x)=0],pivarForm); /d \ /d \ BCpivarForm := ElementInt(|-- u(x)| |-- ut(x)|) \dx / \dx / - BoundaryInt(BdNx q ut(x)) + ElementInt(vt(x) u(x)) /d \ /d \ + ElementInt(|-- v(x)| |-- vt(x)|) = 0 \dx / \dx / > eqns:=test_subs([ut(x),vt(x)],test(x),BCpivarForm): > eqns[1];eqns[2]; /d \ /d \ ElementInt(|-- u(x)| |-- test(x)|) - BoundaryInt(BdNx q test(x)) = 0 \dx / \dx / /d \ /d \ ElementInt(test(x) u(x)) + ElementInt(|-- v(x)| |-- test(x)|) = 0 \dx / \dx /