Field Calculations of High Accuracy by BEM Using Extrapolation

Abstract

For ray tracing with high accuracy and for the possible application of higher order ray tracing algorithms, field calculations are needed with a precision of better than 10^-10. Since field calculations using the boundary element method (BEM) can be easily performed for a given number of boundary elements, we have explored the feasibility and the improvement of accuracy by extrapolation to arbitrary fine discretisation. As examples for electrostatic fields we investigated a spherical condenser and specially shaped cans, where the exact fields are known. By doubling the number of elements, BEM calculations usually improve by more than a factor of 4 in accuracy, as shown by our examples. However, improvements by orders of magnitude become possible by extrapolating a set of two or more calculations with increasing number of elements. For a spherical condensor and a magnetic lens we can demonstrate, how even artifacts, originating from insufficient numerical analysis, are suppressed by the extrapolation technique.