  In this paper, we present a GPU-accelerated direct-sum boundary integral
method to solve the linear Poisson-Boltzmann (PB) equation. In our method, a
well-posed boundary integral formulation is used to ensure the fast convergence
of Krylov subspace based linear algebraic solver such as the GMRES. The
molecular surfaces are discretized with flat triangles and centroid
collocation. To speed up our method, we take advantage of the parallel nature
of the boundary integral formulation and parallelize the schemes within CUDA
shared memory architecture on GPU. The schemes use only $11N+6N_c$
size-of-double device memory for a biomolecule with $N$ triangular surface
elements and $N_c$ partial charges. Numerical tests of these schemes show
well-maintained accuracy and fast convergence. The GPU implementation using one
GPU card (Nvidia Tesla M2070) achieves 120-150X speed-up to the implementation
using one CPU (Intel L5640 2.27GHz). With our approach, solving PB equations on
well-discretized molecular surfaces with up to 300,000 boundary elements will
take less than about 10 minutes, hence our approach is particularly suitable
for fast electrostatics computations on small to medium biomolecules.
