Computation of time and space derivatives in a CQM-based BEM formulation
This work proposes an approach for the numerical computation of time and space derivatives of the time-domain solution of scalar wave propagation problems by means of a boundary element method formulation. Here, this formulation employs the so-called convolution quadrature method. Non-homogeneous initial conditions are taken into account by means of a general procedure, known as initial condition pseudo-force procedure, which replaces the initial conditions by equivalent pseudo-forces. The boundary integral equation with initial conditions contribution is differentiated analytically and the quadrature weights of the standard formulation are transformed in order to compute time and space derivatives at interior points. Numerical examples are presented to show the efficiency of the implemented formulation.
space derivatives boundary element method convolution quadrature method initial condition pseudo-force procedure wave equation time derivative