New developments on the combined application of charge simulation and numerical methods for the computation of electric fields

A new mathematical treatment is proposed to the hybrid method of charge simulation and finite differences for the computation of electric fields, entirely applicable to the similar hybrid method of charge simulation and finite elements. The resulting system of linear equations is solved by making use of the fixed point theory, the QR decomposition (by using the modified Gram-Schmidt method) and the conjugate gradients squared method with a preconditioning technique. New procedures are suggested for the discretization of the boundary conditions, which lead to results with higher precision. Case studies are included.<
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