Efficiency and accuracy are two major concerns in numerical solutions of the Poisson-Boltzmann equation for applications in chemistry and biophysics.Recent developments in boundary element methods,interface methods,ad...Efficiency and accuracy are two major concerns in numerical solutions of the Poisson-Boltzmann equation for applications in chemistry and biophysics.Recent developments in boundary element methods,interface methods,adaptive methods,finite element methods,and other approaches for the Poisson-Boltzmann equation as well as related mesh generation techniques are reviewed.We also discussed the challenging problems and possible future work,in particular,for the aim of biophysical applications.展开更多
In the present paper, compactions of time-dependent viscous granular materials are simulated step by step using the automatic adaptive mesh generation schemes. Inertial forces of the viscous incompressible aggregates ...In the present paper, compactions of time-dependent viscous granular materials are simulated step by step using the automatic adaptive mesh generation schemes. Inertial forces of the viscous incompressible aggregates axe taken into account. The corresponding conservation equations, the weighted-integral formulations, and penalty finite element model are investigated. The fully discrete finite element equations for the simulation are derived. Polygonal particles of aggregates are simplified as mixed three-node and four-node elements. The automatic adaptive mesh generation schemes include contact detection algorithms, and mesh upgrade schemes. Solu- tions of the numerical simulation axe in good agreement with some results from literatures. With minor modification, the proposed numerical model can be applied in several industries, including the pharmaceutical, ceramic, food, and household product manufacturing.展开更多
基金the NIH,NSF,the Howard Hughes Medical Institute,National Biomedical Computing Resource,the NSF Center for Theoretical Biological Physics,SDSC,the W.M.Keck Foundation,and Accelrys,Inc.Michael Holst was supported in part by NSF Awards 0411723,0511766,and 0225630,and DOE Awards DEFG02-05ER25707 and DE-FG02-04ER25620.
文摘Efficiency and accuracy are two major concerns in numerical solutions of the Poisson-Boltzmann equation for applications in chemistry and biophysics.Recent developments in boundary element methods,interface methods,adaptive methods,finite element methods,and other approaches for the Poisson-Boltzmann equation as well as related mesh generation techniques are reviewed.We also discussed the challenging problems and possible future work,in particular,for the aim of biophysical applications.
基金supported by the National Natural Science Foundation of China (No. 10972162)
文摘In the present paper, compactions of time-dependent viscous granular materials are simulated step by step using the automatic adaptive mesh generation schemes. Inertial forces of the viscous incompressible aggregates axe taken into account. The corresponding conservation equations, the weighted-integral formulations, and penalty finite element model are investigated. The fully discrete finite element equations for the simulation are derived. Polygonal particles of aggregates are simplified as mixed three-node and four-node elements. The automatic adaptive mesh generation schemes include contact detection algorithms, and mesh upgrade schemes. Solu- tions of the numerical simulation axe in good agreement with some results from literatures. With minor modification, the proposed numerical model can be applied in several industries, including the pharmaceutical, ceramic, food, and household product manufacturing.
