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We obtain cubature formulas of volume potentials over bounded domainscombining the basis functions introduced in the theory of approximateapproximations with their integration over the tangential-halfspace. Then thecomputation is reduced to the quadrature of one dimensional integrals over thehalfline. We conclude the paper providing numerical tests which show that theseformulas give very accurate approximations and confirm the predicted order ofconvergence.

Computation of volume potentials over bounded domains via approximate approximations