Build a Simple .e File:
Define a very simple 2D PDE problem using the PDELab editors.
The first Easy Session showed you how to load a sample problem, solve it and visualize the solution. In this session, we use the PDELab editors to define a very simple PDE problem from scratch, and then solve it. Click here for a mathematical definition of the problem we will solve.

In this WebPDELab session, we

Afterwards, follow steps 5 though 15 in An Easy Session to solve this problem and visualize the solution.
Step 1. As soon as you connect to the WebPDELab server you see this.

Step 2. Choose 2-D and FDM in the top level window. You see this.

Step 3. Click on New File. You see this.

Step 4. Click on the Framework Editor icon. The Framework Editor starts up and you see this.

Step 5. Click on the button labeled PDE System. An equation window appears.
You will enter the Laplace operator (and force PDELab to compute the right-hand-side.) In the entry field under Operators, type uxx+uyy.
You see this. Click on Done.

Step6. You will enter a true solution and force PDELab to compute the corresponding right-hand-side for your Laplace operator.
Click on the button labeled Forcing Solution and enter our true solution in the entry field: cos(x)*sin(y).
You see this. Click on OK

Step 7. Click on the button labeled Generate Framework. MAXIMA is used to compute the right-hand-side function.
Maxima also generates a .e file containing your equation, the Fortran function definitions of true and force, and a default rectangular domain with coarse grid.
You see this. Choose Quit from the File menu to exit the Framework Editor.

Step 8. Click on the Domain Editor icon. The Domain Editor starts up and you see this.

Step 9. Click on Clear to remove the default boundary. Click on Set Range to enter a new X-Y range for our domain.
In the range box entry field, type -3 3 -3 3 . You see this. Click on Continue.

Step 10. Click on New Rectangle and type -3 3 -3 3 in the entry field.
You see this. Click on Continue. To save this new domain definition to the session, click on the Save button.
We will not change the default boundary conditions; they are Dirichlet, with u=true(x,y) on all four sides.

Step 11. Iconify the Domain Editor and the Log window (so that the WebPDELab server window is not overcrowded.) You see this.

Step 12. Click on the Grid Editor icon. The Grid Editor starts up and you see this.

Step 13. You will specify a 100x100 uniform grid. Click on Uniform Grid, and enter 100. You see this.
Click on Continue.

Step 14. Click on the Mode:X button; it will change to Mode:Y. Click on Uniform Grid, and enter 100. You see this.

Step 15. Click on Continue. You see this. To save this new grid definition to the session, click on the Save button. Then click on Quit.

Step 16. You can now close the Domain Editor. Click on the iconified boundary, and then click on Quit.

Step 17. . We want to use the default 5 point star discretizer module, but we select a new linear solver.
Click on the Soln Menu icon. The current selection for linear solver is jacobi cg, it is shown with its parameters. You see this.

Step 18. Click and hold on the Available Options menu. Choose jacobi si. You see this.
The linear solver jacobi si is shown with its parameters. We will use the default settings for the paramters.
Click on the button Save & Quit. The new module selection is saved to the session.

Step 19. Click on the Output Specifications Editor icon. The Output Editor starts up.
Click on the Output Filename button and type test.out. You see this. Click on Continue.

Step 20. Click on the Plot Function button and select u from the drop down menu.
Click on Continue to save the output requirments information to the session.

Step 21. The .e file now contains a complete description of the PDE problem.
You can execute this problem and visualize the solution as in An Easy Session, steps 5-15.
A brief summary of problem execution and solution visualization is given here.

Step 22.Click on the ExecuteTool icon. You see this.
Click on the Run button. After a few seconds, you see this. Click on the Quit button.

Step 23. Click on the OutputTool icon. You see this.
Select Load File from the File menu, and make sure only //ELLPACK Solution is selected. You see this.
Click on OK. Select test.out from the file menu and click on OK. A Solution Selection Panel pops up.
Click on u on the Solutions Selection Panel. You see this. Click on OK.
Click on the Visual2D button in the OutputTool window, and then Run Tool.
The solution will appear in the plot window. You see this.
Click on Quit in the plot window and choose Quit from the File menu of the OutputTool.

Step 24.To exit this PDELab session, click on Quit in the session window.