Description

EVALEXPR Evaluate expression in specified points.

[ VEVAL ] = EVALEXPR( S_EXPR, XP, PROB, SOLNUM, EVAL_TYPE, TOL ) Evaluates the expression S_EXPR in the points XP, 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").

XP is a row array of evaluation points (size n_sdim rows by n_evaluation_points columns). For example using XP = PROB.grid.p evaluates the expression in all grid points.

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)").

The optional EVAL_TYPE flag toggles evaluation method (default 1)

0 - Full FEM shape function evaluation for all points (slow, accurate).

1 - Like (0) but with fast vectorized evaluation of dependent variables defined by Lagrange P0-P2 FEM shape functions (PROB.sfun).

2 - Evaluation via interpolation to grid points (tri/tet grids, fast but less accurate). Invalid/NaN values contribute zero/0 to the output.

3 - Like (2) above but also allow invalid/NaN values in output.

TOL is a tolerance used by ismembertol/deduplicate to determine which evaluation points in XP are aligned with grid points and can be evaluated faster and more efficiently. Use EVALEXPRP instead of EVALEXPR for directly evaluating an expression in all grid/mesh points (PROB.grid.p) at the same time.

The resulting evaluated values are returned in a column vector VEVAL with one value for each evaluation point. Points outside the grid/geometry will by default return invalid/NaN (Not-a-Number) values. The resulting values can then be saved/exported in various formats using built-in functions such as SAVE, CSVWRITE, and XLSWRITE.

Input       Value/[Size]           Description
-----------------------------------------------------------------------------------
s_expr      string                 Expression to evaluate
xp          [n_sdim,n_xp]          Coordinates of evaluation points
prob        struct                 FEA model/problem definition struct
solnum      scalar int {n_sols}    Solution number/time to evaluate
eval_type   scalar int {1}         Evaluation type
                                      0 - Standard/full evaluation
                                      1 - Vectorized evaluation for dep. variables
                                      2 - Linear interpolation via nodes (fast)
                                      3 - Like 2 and allow invalid (NaN) values
tol         scalar  {1e-5}         Tolerance for evaluation/grid aligned points
                                                                                  .
Output      Value/(Size)           Description
-----------------------------------------------------------------------------------
vEval       [n_xp,1]               Output/result vector of evaluated values

Examples

  1) Evaluate the dependent variable "u" in the point x=0.5.

  fea = ex_poisson1('iplot', false);  % Use example script to generate FEA data struct.

  u_0p5 = evalexpr('u', 0.5, fea)

  2) Evaluate and plot the expression "1+sin(ux)" at the line x=-1:1, y=0.

  fea = ex_poisson2('iplot', false);

  p = [linspace(-1, 1, 100); zeros(1, 100)];
  result = evalexpr('1+sin(ux)', p, fea);

  plot(p(1,:), result)

  3) Evaluate the mean of the temperature derivative in the mesh points at time t=100 s.

  fea = ex_heattransfer5('iplot', false);
  solnum = find(fea.sol.t == 100);

  magTx = evalexpr('sqrt(Tx^2 + Ty^2)', fea.grid.p, fea, solnum);
  mean(magTx)

See also: evalexprp

evalexpr.m File Reference

Description