Jiahui Chen

selected publications

1. JCP

   On preconditioning the treecode-accelerated boundary integral (TABI) Poisson–Boltzmann solver

   Jiahui Chen, and Weihua Geng

   Journal of Computational Physics 2018

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   We recently developed a treecode-accelerated boundary integral (TABI) solver for solving Poisson–Boltzmann (PB) equation [1]. The solver has combined advantages in accuracy, efficiency, memory, and parallelization as it applies a well-posed boundary integral formulation to circumvent many numerical difficulties associated with the PB equation and uses an O(NlogN) treecode to accelerate the GMRES iterative solver. However, as observed in our previous work, occasionally when the mesh generator produces low quality triangles, the number of GMRES iterations required to solve the discretized boundary integral equations Ax=b could be large. To address this issue, we design a preconditioning scheme using preconditioner matrix M such that M^-1A has much improved condition while M^-1z can be rapidly computed for any vector z. In this scheme, the matrix M carries the interactions between boundary elements on the same leaf only in the tree structure thus is block diagonal with many computational advantages. The sizes of the blocks in M are conveniently controlled by the treecode parameter N0, the maximum number of particles per leaf. The numerical results show that this new preconditioning scheme improves the TABI solver with significantly reduced iteration numbers and better accuracy, particularly for protein sets on which TABI solver previously converges slowly. In addition, this preconditioning scheme potentially can improve the condition number of various multipole method accelerated boundary elements solvers in scattering, fluids, elasticity, etc.

2. DCDS–B

   Evolutionary de Rham-Hodge method

   Jiahui Chen, Rundong Zhao, Yiying Tong, and 1 more author

   Discrete and Continuous Dynamical Systems Series B 2021

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   The de Rham-Hodge theory is a landmark of the 20th Century’s mathematics and has had a great impact on mathematics, physics, computer science, and engineering. This work introduces an evolutionary de Rham-Hodge method to provide a unified paradigm for the multiscale geometric and topological analysis of evolving manifolds constructed from a filtration, which induces a family of evolutionary de Rham complexes. While the present method can be easily applied to close manifolds, the emphasis is given to more challenging compact manifolds with 2-manifold boundaries, which require appropriate analysis and treatment of boundary conditions on differential forms to maintain proper topological properties. Three sets of unique evolutionary Hodge Laplacians are proposed to generate three sets of topology-preserving singular spectra, for which the multiplicities of zero eigenvalues correspond to exactly the persistent Betti numbers of dimensions 0, 1, and 2. Additionally, three sets of non-zero eigenvalues further reveal both topological persistence and geometric progression during the manifold evolution. Extensive numerical experiments are carried out via the discrete exterior calculus to demonstrate the potential of the proposed paradigm for data representation and shape analysis. To demonstrate the utility of the proposed method, application is considered to the protein B-factor predictions of a few challenging cases for which other existing models do not work well.

3. CPC

   Cyclically parallelized treecode for fast computations of electrostatic interactions on molecular surfaces

   Jiahui Chen, Weihua Geng, and Daniel R Reynolds

   Computer Physics Communications 2021

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   We study the parallelization of a flexible order Cartesian treecode algorithm for evaluating electrostatic potentials of charged particle systems in which particles are located on the molecular surfaces of biomolecules such as proteins. When the well-separated condition is satisfied, the treecode algorithm uses a far-field Taylor expansion to compute O(NlogN) particle–cluster interactions to replace the O(N^2) particle–particle interactions. The algorithm is implemented using the Message Passing Interface (MPI) standard by creating identical tree structures in the memory of each task for concurrent computing. We design a cyclic order scheme to uniformly distribute spatially-closed target particles to all available tasks, which significantly improves parallel load balancing. We also investigate the parallel efficiency subject to treecode parameters such as Taylor expansion order p, maximum particles per leaf N0, and maximum acceptance criterion theta. This cyclically parallelized treecode can solve interactions among up to tens of millions of particles. However, if the problem size exceeds the memory limit of each task, a scalable domain decomposition (DD) parallelized treecode using an orthogonal recursive bisection (ORB) tree can be used instead In addition to efficiently computing the N-body problem of charged particles, our approach can potentially accelerate GMRES iterations for solving the boundary integral Poisson–Boltzmann equation.

4. JCP

   A Cartesian FMM-accelerated Galerkin boundary integral Poisson-Boltzmann solver

   Jiahui Chen, Johannes Tausch, and Weihua Geng

   Journal of Computational Physics 2023

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   The Poisson-Boltzmann model is an effective and popular approach for modeling solvated biomolecules in continuum solvent with dissolved electrolytes. In this paper, we report our recent work in developing a Galerkin boundary integral method for solving the linear Poisson-Boltzmann (PB) equation. The solver has combined advantages in accuracy, efficiency, and memory usage as it applies a well-posed boundary integral formulation to circumvent many numerical difficulties associated with the PB equation and uses an Cartesian Fast Multipole Method (FMM) to accelerate the GMRES iteration. In addition, special numerical treatments such as adaptive FMM order, block diagonal preconditioners, Galerkin discretization, and Duffy’s transformation are combined to improve the performance of the solver, which is validated on benchmark Kirkwood’s sphere and a series of testing proteins.