Using CutFEM for solving the linearized Poisson-Boltzmann equation: Introductory application in HiFlow3

Abstract

The Poisson-Boltzmann equation(PBE) is a fundamental equation for accurate description of electrostatics in ionic solutions or plasma. Hence, it finds application in a wide variety of fields including plasma physics, computational biology, colloidal and interface science and chemistry. In this preprint, we describe a first approach for solving it in a linearized setup using the CutFEM method in the software framework HiFlow3. The considered methods are easy to use, but not oriented towards extracting optimal computing time. Forthis purpose,the weak form of the linear PBE is first derived. Then, the CutFEM based numerical method is proposed. Finally, the most important code sections in HiFlow 3 are explained in more details. The electrostatic potential for ubiquitin and the adenovirus virion molecules are calculated and presented in a numerical example at the end of the paper.