BIT Numerical Mathematics

, Volume 47, Issue 4, pp 853-871

First online:

A new minimization protocol for solving nonlinear Poisson–Boltzmann mortar finite element equation

  • Dexuan XieAffiliated withDepartment of Mathematical Sciences, University of Wisconsin Email author 
  • , Shuzi ZhouAffiliated withDepartment of Applied Mathematics, Hunan University

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The nonlinear Poisson–Boltzmann equation (PBE) is a widely-used implicit solvent model in biomolecular simulations. This paper formulates a new PBE nonlinear algebraic system from a mortar finite element approximation, and proposes a new minimization protocol to solve it efficiently. In particular, the PBE mortar nonlinear algebraic system is proved to have a unique solution, and is equivalent to a unconstrained minimization problem. It is then solved as the unconstrained minimization problem by the subspace trust region Newton method. Numerical results show that the new minimization protocol is more efficient than the traditional merit least squares approach in solving the nonlinear system. At least 80 percent of the total CPU time was saved for a PBE model problem.

Key words

Poisson–Boltzmann equation mortar finite element nonlinear system unconstrained minimization biomolecular simulations