#Example_321 A Simple boundary element example fem fem define node;r;simplebem;example #Read in the nodes for a simple BEM problem fem define window;c #Calculate the window size fem draw nodes #Draw the nodes fem define base;p #Define a boundary element basis. Define # ! 1 Boundary element Lagrange/Hermite # ! tensor product basis with 1 xi direction # ! and quadratic Lagrange interpolation. # ! Default all other options. fem list base #List the basis function fem list base family 1 #List the all the basis functions associated # ! with the various quadrature schemes # ! required for BEM. fem define elem;p #Define 4 quadratic (3 local nodes) elements. # ! With boundary elements we need to take # ! care with which way our Xi direction # ! goes in order to correctly define the # ! OUTWARD normal for the mesh. In cmiss # ! the convention is that as we move along # ! in increasing Xi the interior of the # ! mesh domain is kept to the right. Hence # ! for this case, where the solution domain # ! is the interior of a circle, the direction # ! of increasing Xi must be clockwise. The # ! local nodes for each element are hence: # ! Element 1 - 1,8,7; Element 2 - 7,6,5; # ! Element 3 - 5,4,3; and Element 4 - 3,2,1. fem draw lines #Draw the lines fem draw gauss #Draw the Gauss points fem define equation;p #Define a Static Analysis (Standard) # ! Laplace's Equation using Direct Boundary # ! elements. Default all other options fem define materials;p #Define (no) materials. fem define initial;p #Define the boundary conditions. For # ! boundary elements you have two unknowns # ! each node - the variable (e.g temperature) # ! and its normal derivative (e.g. heat flux) # ! and you must specify exactly one of these # ! at each node. Specify temperature # ! essential boundary conditions of: # ! Node 1 - 10; Nodes 2,8 - 5; Nodes 3,7 - 0 # ! and flux boundary conditions of: # ! Nodes 4,5,6 - 0. fem define solve;p #Define the solve options. # ! Default for all questions. fem solve #Solve the boundary value problem. fem list node solution #List the nodal solutions (temperatures). fem list node flux #List the nodal fluxes.

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