Extending the fast multipole method for charges inside a dielectric sphere in an ionic solvent: High-order image approximations for reaction fields
✍ Scribed by Shaozhong Deng; Wei Cai
- Publisher
- Elsevier Science
- Year
- 2007
- Tongue
- English
- Weight
- 351 KB
- Volume
- 227
- Category
- Article
- ISSN
- 0021-9991
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✦ Synopsis
As a sequel to our previous paper on extending the Fast Multipole Method (FMM) for charges inside a dielectric sphere [J. Comput. Phys. 223 (2007) 846-864], this paper further extends the FMM to the electrostatic calculation for charges inside a dielectric sphere immersed in an ionic solvent, a scenery with more relevance in biological applications. The key findings include two fourth-order multiple discrete image approximations in terms of u = ka to the reaction field induced by the ionic solvent, provided that u = ka < 1 where k is the inverse Debye screening length of the ionic solvent and a is the radius of the dielectric sphere. A 10 À4 relative accuracy in the reaction field of a source charge within the sphere can be achieved with only 3-4 point image charges. Together with the image charges, the FMM can be used to speed up the calculation of electrostatic interactions of charges in a dielectric sphere immersed in an ionic solvent.