Description

INTSUBD Integrate expression over subdomains.

[ VAL ] = INTSUBD( S_EXPR, PROB, IND_S, IND_C, I_CUB, SOLNUM ) Integrates the expression S_EXPR over subdomains, using FEM interpolation of data given in the FEA model/problem struct PROB.

The string expression S_EXPR must be valid MATLAB syntax, and may include combinations of dependent variables (defined in PROB.dvar) and derivatives, space dimensions (PROB.sdim), and all common built-in constants and mathematical functions available, such as pi, eps, sqrt, sin, cos, log, exp, abs etc (for example "sin(2*pi*x + ux^2)" where "ux" is the x-derivative of the dependent variable "u").

The optional vector IND_S are indices to subdomains to include in the evaluation (default all, "unique(PROB.grid.s)"), or alternatively IND_C can be provided with indices to specific grid/mesh cells to perform evaluation in (default all, "1:size(PROB.grid.c, 2)").

SOLNUM is an optional scalar integer indicating the solution/time to use in the evaluation (PROB.sol.u(:,SOLNUM), defaults to the last available solution "size(PROB.sol.u, 2)").

Returns the integration result VAL.

Input       Value/[Size]           Description
-----------------------------------------------------------------------------------
s_expr      string                 Expression to integrate
prob        struct                 FEA model/problem definition struct
ind_s       [1,n_subd]             Subdomain numbers (default all)
ind_c       [1,n_cells]            Cell indices (default all)
i_cub       scalar int             Evaluation point rule/quadrature order (default 2)
solnum      scalar int {n_sols}    Solution number/time to evaluate
                                                                                  .
Output      Value/[Size]           Description
-----------------------------------------------------------------------------------
val         scalar                 Result of integration

Examples

  1) Integrate "1" (= area) on a unit circle.

  fea = ex_poisson2('iplot', false);  % Use example script to generate FEA data struct.

  A = intsubd('1', fea)

  2) Integrate "sqrt(ux^2 + uy^2)" for the Poisson equation on a unit circle.

  fea = ex_poisson2('iplot', false);

  mag_u = intsubd('sqrt(ux^2 + uy^2)', fea)

See also: intbdr, minmaxbdr, minmaxsubd

intsubd.m File Reference

Description