### AFMPB: an adaptive fast multipole Poisson–Boltzmann solver for calculating electrostatics in biomolecular systems

- Comput. Phys. Commun

"... ii ..."

### Analytical nonlocal electrostatics using eigenfunction expansion of boundary-integral operators

- Molecular Based Mathematical Biology

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### 1 Mathematical Analysis of the BIBEE Approximation for Molecular Solvation: Exact Results for Spherical Inclusions

, 2011

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### Complexes Using Inverse Methods, Combinatorial Search,

, 2006

"... requirements for the degree of ..."

### ROBUST FINITE ELEMENT SOLVER FOR MOLECULAR ELECTROSTATIC ENERGY COMPUTATIONS Dissertation zur Erlangung des akademischen Grades des Doktors der Naturwissenschaften (Dr. rer. nat.)

"... This dissertation is dedicated to my lovely universe, Elif, who gives me my energy in life to keep on doing the things I’m doing especially while my research in scientific computing over the past years. This work got the icing on the cake by my daughter, Melina, who was born during this work and mak ..."

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This dissertation is dedicated to my lovely universe, Elif, who gives me my energy in life to keep on doing the things I’m doing especially while my research in scientific computing over the past years. This work got the icing on the cake by my daughter, Melina, who was born during this work and makes me smile every day, repeatedly.

### Numerical Solution of Boundary Integral Equations for Molecular Electrostatics

"... Abstract In this paper we evaluate two approaches to discretizing integral-equation formulations of linear, continuum models for estimating intra-and intermolecular electrostatic interactions in solution. The importance of electrostatic forces in a variety of biological and chemical processes has m ..."

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Abstract In this paper we evaluate two approaches to discretizing integral-equation formulations of linear, continuum models for estimating intra-and intermolecular electrostatic interactions in solution. The importance of electrostatic forces in a variety of biological and chemical processes has motivated extensive research into numerical simulation techniques. Boundary-element methods (BEM) represent one popular approach to simulating models based on partial-differential equations (PDEs), and give rise to linear matrix equations. The entries associated with BEM matrices can be calculated in different ways, and in this paper we show that a straightforward approach to discretizing the widely used apparent-surface-charge (ASC) formulation is significantly less accurate than an equivalent but less obvious approach. In contrast, more computationally expensive boundaryintegral formulations based on pairs of coupled integral equations exhibit reduced sensitivity to the approach to forming the BEM matrix. We also illustrate the equivalence between the ASC formulation and the double-layer formulation derived by Juffer et al.; when their matrix entries are evaluated appropriately, the two formulations produce numerically identical solutions. A similar equivalence exists between the Yoon-Lenhoff and the Bordner-Huber formulations.

### Mathematical Models for Biomolecule Analysis and Design

, 2006

"... This thesis presents a set of numerical techniques that extend and improve computational modeling approaches for biomolecule analysis and design. The presented research focuses on surface formulations of modeling problems related to the estimation of the energetic cost to transfer a biomolecule from ..."

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This thesis presents a set of numerical techniques that extend and improve computational modeling approaches for biomolecule analysis and design. The presented research focuses on surface formulations of modeling problems related to the estimation of the energetic cost to transfer a biomolecule from the gas phase to aqueous solution. The thesis discusses four contributions to modeling biomolecular interactions. First, the thesis presents an approach to allow accurate discretization of the most prevalent mathematical definitions of the biomolecule–solvent interface; also presented are a number of accurate techniques for numerically integrating possibly singular

### Efficient Optimization of Electrostatic Interactions Between

"... Abstract — We present a PDE-constrained approach to optimizing the electrostatic interactions between two biomolecules. These interactions play important roles in the determination of binding affinity and specificity, and are therefore of significant interest when designing a ligand molecule to bind ..."

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Abstract — We present a PDE-constrained approach to optimizing the electrostatic interactions between two biomolecules. These interactions play important roles in the determination of binding affinity and specificity, and are therefore of significant interest when designing a ligand molecule to bind tightly to a receptor. Using a popular continuum model and physically reasonable assumptions, the electrostatic component of the binding free energy is a convex, quadratic function of the ligand charge distribution. Traditional optimization methods require exhaustive pre-computation, and the expense has precluded a full exploration of the promise of electrostatic optimization in biomolecule analysis and design. In this paper we describe an approach in which the electrostatic simulations and optimization problem are solved simultaneously; unlike many PDEconstrained optimization frameworks, the proposed method does not incorporate the PDE as a set of equality constraints. This co-optimization approach can be used by itself to solve unconstrained problems or those with linear equality constraints, or in conjunction with primal–dual interior point methods to solve problems with inequality constraints. Model problems demonstrate that the co-optimization method is computationally efficient and that it can be used to solve realistic problems. I.

### Keywords:

, 2015

"... ava i lable at www.sciencedirect.com journal homepage: www.europeanurology.com Article info Article history: ..."

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ava i lable at www.sciencedirect.com journal homepage: www.europeanurology.com Article info Article history:

### The pFFT accelerated BEM for the simulation of 3-D acoustic problems

"... The precorrected-FFT acceleration technique is successfully applied in the boundary element method for the simulation of 3-D acoustic radiation problems. The constant triangular element is employed in the simulation. The computational cost, the consumed memory and the accuracy of the current method ..."

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The precorrected-FFT acceleration technique is successfully applied in the boundary element method for the simulation of 3-D acoustic radiation problems. The constant triangular element is employed in the simulation. The computational cost, the consumed memory and the accuracy of the current method are demonstrated and analyzed through the simulation of the acoustic radiation from a pulsating sphere. Both the surface and the exterior field dimensionless acoustic pressures are presented to show the precision of this method.