A Practical Guide to Boundary Element Methods with the Software Library BEMLIB

Pozrikidis, C.

doi:10.1201/9781420035254

Cited by 272 publications

(202 citation statements)

References 0 publications

Supporting

Mentioning

201

Contrasting

Unclassified

Order By: Relevance

“…͑4.4.5͒ in Ref. 19. This is the value we take in our case, because we consider that our molecular boundary has been smoothed before discretization.…”

Section: ͑11͒mentioning

confidence: 99%

Calculation of the Maxwell stress tensor and the Poisson-Boltzmann force on a solvated molecular surface using hypersingular boundary integrals

Cheng

Hou

et al. 2005

The Journal of Chemical Physics

View full text Add to dashboard Cite

The electrostatic interaction among molecules solvated in ionic solution is governed by the Poisson-Boltzmann equation (PBE). Here the hypersingular integral technique is used in a boundary element method (BEM) for the three-dimensional (3D) linear PBE to calculate the Maxwell stress tensor on the solvated molecular surface, and then the PB forces and torques can be obtained from the stress tensor. Compared with the variational method (also in a BEM frame) that we proposed recently, this method provides an even more efficient way to calculate the full intermolecular electrostatic interaction force, especially for macromolecular systems. Thus, it may be more suitable for the application of Brownian dynamics methods to study the dynamics of protein/protein docking as well as the assembly of large 3D architectures involving many diffusing subunits. The method has been tested on two simple cases to demonstrate its reliability and efficiency, and also compared with our previous variational method used in BEM.

show abstract

“…͑4.4.5͒ in Ref. 19. This is the value we take in our case, because we consider that our molecular boundary has been smoothed before discretization.…”

Section: ͑11͒mentioning

confidence: 99%

Calculation of the Maxwell stress tensor and the Poisson-Boltzmann force on a solvated molecular surface using hypersingular boundary integrals

Cheng

Hou

et al. 2005

The Journal of Chemical Physics

View full text Add to dashboard Cite

show abstract

“…In addition, part of the calculation procedure mentioned in the Appendix (switching between nodal points → middle points of line elements → nodal points 35 ) also helps stabilize the interface.…”

Section: Numerical Simulations With Boundary Integral Methodsmentioning

confidence: 99%

“…The boundary integral method provides an efficient way to solve incompressible and irrotational flows 34,35 , which in my case allows me to solve for u in the exterior fluid given the potential on the boundary. This method is based on the following Green's function formulation that associates the velocity potential with the normal velocity on the air-water interface:…”

Section: Numerical Simulations With Boundary Integral Methodsmentioning

confidence: 99%

Curvature singularity in the asymmetric breakup of an underwater air bubble

Lai

2012

Physics of Fluids

View full text Add to dashboard Cite

The presence of slight azimuthal asymmetry in the initial shape of an underwater bubble entirely alters the final breakup dynamics. Here I examine the influence of initial asymmetry on the final breakup by simulating the bubble surface evolution as a Hamiltonian evolution corresponding to an inviscid, two-dimensional, planar implosion. I find two types of breakups: a previously reported coalescence mode in which distant regions along the air-water surface curve inwards and eventually collide with finite speed, and a hitherto unknown cusp-like mode in which the surface develops sharp tips whose radii of curvature are much smaller than the average neck radius.I present three sets of results that characterize the nature of this cusp mode. First, I show that the cusp mode corresponds to a saddle-node. In other words, an evolution towards a cross-section shape with sharp tips invariably later evolves away from it. In phase space, this saddle-node separates coalescence modes whose coalescence planes lie along different spatial orientations. Second, I show that the formation of the sharp tips can be interpreted as a weakly first-order transition which becomes second-order, corresponding to the formation of a finite-time curvature singularity, in the limit that the initial perturbation amplitude approaches zero. Third I show that, as the curvature singularity is approached, the maximum surface curvature diverges approximately as (t c − t) −0.8 , where t c is the onset time of the singularity and the maximum velocity diverges approximately as (t c − t) −0.4 . In practice, these divergences imply that viscous drag and compressibility of the gas flow, two effects not included in my analysis, become significant as the interface evolves towards the curvature singularity.PACS numbers: 47.55.df, 47.20.Cq, 47.20.Ma

show abstract

“…When the element E t contains x p , the principal-value integral should be applied, and through transformation, the Gaussian quadrature can also be used. 20 For clarity, matrix and vector representations will be used from now on. Let's us denote matrix H as…”

Section: A Numerical Solution For a Single Molecule Systemmentioning

confidence: 99%

Computation of electrostatic forces between solvated molecules determined by the Poisson–Boltzmann equation using a boundary element method

Zhang

McCammon

2005

The Journal of Chemical Physics

101

View full text Add to dashboard Cite

A rigorous approach is proposed to calculate the electrostatic forces among an arbitrary number of solvated molecules in ionic solution determined by the linearized Poisson-Boltzmann equation. The variational principle is used and implemented in the frame of a boundary element method ͑BEM͒. This approach does not require the calculation of the Maxwell stress tensor on the molecular surface, therefore it totally avoids the hypersingularity problem in the direct BEM whenever one needs to calculate the gradient of the surface potential or the stress tensor. This method provides an accurate and efficient way to calculate the full intermolecular electrostatic interaction energy and force, which could potentially be used in Brownian dynamics simulation of biomolecular association. The method has been tested on some simple cases to demonstrate its reliability and efficiency, and parts of the results are compared with analytical results and with those obtained by some known methods such as adaptive Poisson-Boltzmann solver.

show abstract

A Practical Guide to Boundary Element Methods with the Software Library BEMLIB

Cited by 272 publications

References 0 publications

Calculation of the Maxwell stress tensor and the Poisson-Boltzmann force on a solvated molecular surface using hypersingular boundary integrals

Calculation of the Maxwell stress tensor and the Poisson-Boltzmann force on a solvated molecular surface using hypersingular boundary integrals

Curvature singularity in the asymmetric breakup of an underwater air bubble

Computation of electrostatic forces between solvated molecules determined by the Poisson–Boltzmann equation using a boundary element method

Contact Info

Product

Resources

About