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The electromagnetic field can diverge near sharp corners separating continuous media. This is a mathematical pathology that is inherent to the assumption of local response and sharp boundaries. In the BEM, this is translated into divergences of the boundary sources near sharp corners that can cause numerical instability. In actual physical systems sharp corners do not exist, because atomic distances impose a discrete length of measure. Furthermore, the assumption of local response breaks down at non-physically-small distances. By smoothing sharp corners through some rounding, these problems are solved and one finds a physical connection to the real particle behavior
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The electromagnetic field can diverge near sharp corners separating continuous media. This is a mathematical pathology that is inherent to the assumption of local response and sharp boundaries. In the BEM, this is translated into divergences of the boundary sources near sharp corners that can cause numerical instability. In actual physical systems sharp corners do not exist, because atomic distances impose a discrete length of measure. Furthermore, the assumption of local response breaks down at non-physically-small distances. By smoothing sharp corners through some rounding, these problems are solved and one finds a physical connection to the real particle behavior.
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