Higher-order Far-field Boundary Conditions for Crystalline Defects

Crystalline materials exhibit long-range elastic fields due to the presenceof defects, leading to significant domain size effects in atomisticsimulations. A rigorous far-field expansion of these long-range fieldsidentifies low-rank structure in the form of a sum of discrete multipole termsand continuum correctors. We propose a novel numerical scheme that exploitsthis low-rank structure to accelerate material defect simulations by minimizingthe domain size effects. Our approach iteratively improves the boundarycondition, systematically following the asymptotic expansion of the far field.We provide both rigorous error estimates for the method and a range ofempirical numerical tests, to assess it's convergence and robustness.