Description

INTBDR Integrate expression on boundaries.

[ VAL ] = INTBDR( S_EXPR, PROB, IND_B, I_CUB, SOLNUM, IND_S ) Integrates the expression S_EXPR on boundaries, 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_B are indices to boundaries to include in the evaluation (default all "unique(PROB.grid.b(3,:))").

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)").

IND_S optionally specifies which subdomains to use as reference for internal/interior boundaries (normals point outward from these subdomains).

Returns the integration result VAL.

Input       Value/[Size]           Description
-----------------------------------------------------------------------------------
s_expr      string                 Expression to integrate
prob        struct                 FEA model/problem definition struct
ind_b       [1,n_bdr]              Boundary numbers (default all)
i_cub       scalar int             Evaluation point rule/quadrature order (default 2)
solnum      scalar int {n_sols}    Solution number/time to evaluate
ind_s       integer array          Integration subdomains for internal boundaries
                                                                                  .
Output      Value/[Size]           Description
-----------------------------------------------------------------------------------
val         scalar                 Result of integration

Examples

  1) Integrate "1" (= circumference) around a unit circle.

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

  circ = intbdr('1', fea)

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

  fea = ex_poisson2('iplot', false);

  mag_u_b2 = intsubd('sqrt(ux^2 + uy^2)', fea, 2)

See also: intsubd, minmaxbdr, minmaxsubd

intbdr.m File Reference

Description