MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Chebyshev-Galerkin algorithm for computing 3D Solvation

Gennady Chuev


To solve 3D integral equations of molecular liquids, we have developed a numerical scheme based on the Galerkin method. Using a domain decomposition of the interface region, we reduce the problem to calculations of approximating coefficients and the kernel matrix in spherical shell elements (SSE). Applying the linear transformation of coordinates for each SSE we result in calcualtions of the approximating coefficients in cubic volumes. Using the conventional triple Chebyshev series as a basis set, we derive formulas for calculations of the approximating coefficients and evaluate the computational costs of these operations. We have described the general properties of the Chebyshev-Galerkin matrix and derived analytical expressions for recursion calculations of the matrix elements. We have also outlined an iterative method for the solutions of the nonlinear equations obtained for the approximating coefficients, which is based on the direct inversion in the iterative space. Finally, we have estimated the total computational cost of the proposed scheme and compared it with current algorithms for computing 3D solvation problem. It was found the proposed scheme to be by 2-3 orders effective than the current algorithms based on the uniform FFT.


Related publications

2011 Repository Open Access
Gennady N. Chuev

Chebyshev-Galerkin algorithm for computing 3D solvation