  The Poisson-Boltzmann (PB) model governs the electrostatics of solvated
biomolecules, i.e., potential, field, energy, and force. These quantities can
provide useful information about protein properties, functions, and dynamics.
By considering the advantages of current algorithms and computer hardware, we
focus on the parallelization of the treecode-accelerated boundary integral
(TABI) PB solver using the Message Passing Interface (MPI) on CPUs and the
direct-sum boundary integral (DSBI) PB solver using KOKKOS on GPUs. We provide
optimization guidance for users when the DSBI solver on GPU or the TABI solver
with MPI on CPU should be used depending on the size of the problem.
Specifically, when the number of unknowns is smaller than a predetermined
threshold, the GPU-accelerated DSBI solver converges rapidly thus has the
potential to perform PB model-based molecular dynamics or Monte Carlo
simulation. As practical appliations, our parallelized boundary integral PB
solvers are used to solve electrostatics on selected proteins that play
significant roles in the spread, treatment, and prevention of COVID-19 virus
diseases. For each selected protein, the simulation produces the electrostatic
solvation energy as a global measurement and electrostatic surface potential
for local details.
