User manual MATLAB PARTIAL DIFFERENTIAL EQUATION TOOLBOX 1

[. . . ] Partial Differential Equation ToolboxTM 1 User's Guide How to Contact The MathWorks Web Newsgroup www. mathworks. com/contact_TS. html Technical Support www. mathworks. com comp. soft-sys. matlab suggest@mathworks. com bugs@mathworks. com doc@mathworks. com service@mathworks. com info@mathworks. com Product enhancement suggestions Bug reports Documentation error reports Order status, license renewals, passcodes Sales, pricing, and general information 508-647-7000 (Phone) 508-647-7001 (Fax) The MathWorks, Inc. 3 Apple Hill Drive Natick, MA 01760-2098 For contact information about worldwide offices, see the MathWorks Web site. Partial Differential Equation ToolboxTM User's Guide © COPYRIGHT 1995­2010 The MathWorks, Inc. The software described in this document is furnished under a license agreement. The software may be used or copied only under the terms of the license agreement. [. . . ] For the adaptive mode, the following parameters are available: - Adaptive mode. The maximum number of new triangles allowed (can be set to Inf). A default value is calculated based on the current mesh. 2-23 2 Graphical User Interface - Maximum number of refinements. The maximum number of successive refinements attempted. There are two triangle selection methods, described below. You can also supply your own function. · Worst triangles. This method picks all triangles that are worse than a fraction of the value of the worst triangle (default: 0. 5). This method picks triangles using a relative tolerance criterion (default: 1E-3). Enter the name of a user-defined triangle selection method. See pdedemo7 for an example of a user-defined triangle selection method. · · - Function parameter. The function parameter allows fine-tuning of the triangle selection methods. For the worst triangle method (pdeadworst), it is the fraction of the worst value that is used to determine which triangles to refine. For the relative tolerance method, it is a tolerance parameter that controls how well the solution fits the PDE. See the Parameters dialog box description in "Mesh Menu" on page 2-20. - If the problem is nonlinear, i. e. , parameters in the PDE are directly dependent on the solution u, a nonlinear solver must be used. The following parameters are used: - Use nonlinear solver. Tolerance parameter for the nonlinear solver. Can be a constant or a function of x and y given as a MATLAB expression that can be evaluated on the nodes of the current mesh. Jacobian approximation method: fixed (the default), a fixed point iteration, lumped, a "lumped" (diagonal) approximation, or full, the full Jacobian. - 2-24 Using the pdetool Menus - Norm. The type of norm used for computing the residual. Enter as energy for an energy norm, or as a real scalar p to give the lp norm. The default is Inf, the infinity (maximum) norm. Note The adaptive mode and the nonlinear solver can be used together. - Parabolic PDEs. [. . . ] In case of trouble, If convergence is too slow, try (in this order of priority): · a smaller interval lb, ub · a larger jmax · a larger maxmul If factorization fails, try again with lb or ub finite. Then shift is chosen at random and hopefully not at an eigenvalue. If it fails again, check whether pencil may be singular. If it goes on forever, there may be too many eigenvalues in the strip. [. . . ]