A numerical scheme is described for accurately accommodating oblique,non-aligned, boundaries, on a three-dimensional cartesian grid. The schemegives second-order accuracy in the solution for potential of Poisson's equationusing compact difference stencils involving only nearest neighbors.Implementation for general "Robin" boundary conditions and for boundariesbetween media of different dielectric constant for arbitrary-shaped regions isdescribed in detail. The scheme also provides for the interpolation of field(potential gradient) which, despite first-order peak errors immediatelyadjacent to the boundaries, has overall second order accuracy, and thusprovides with good accuracy what is required in particle-in-cell codes: theforce. Numerical tests on the implementation confirm the scalings and theaccuracy.
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