BEM Numerical Implementation of the Momentum Balance Equations

Similar to scalar problems, the first step of the BEM is to discretize the boundary into a series of elements over which the velocity and traction are assumed to vary according to some interpolation functions. 

Once the boundary is divided into NE elements, eqn. (10.80) will be equivalent to 

The value of any variable at any point within the element is defined in terms of the node s values according to the isoparametric interpolation. As with finite elements, the coordinates and the velocity field for each element can be written as follows 

For any point in the domain and boundary, the fundamental solutions in the boundary integrals of eqn. (10.82) can be written in matrix form as 

By substitution of eqns. (10.88) to (10.91) into eqn. (10.82), the boundary integral formula can be written as follows 

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