Topic
Finite difference method
About: Finite difference method is a research topic. Over the lifetime, 21603 publications have been published within this topic receiving 468852 citations. The topic is also known as: Finite-difference methods & FDM.
Papers published on a yearly basis
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Papers
TL;DR: In this article, a non-periodic Poisson-Boltzmann dynamics method with a nonperiodic boundary condition is proposed for simulation of biomolecules in dilute aqueous solutions.
Abstract: We have developed a well-behaved and efficient finite difference Poisson–Boltzmann dynamics method with a nonperiodic boundary condition. This is made possible, in part, by a rather fine grid spacing used for the finite difference treatment of the reaction field interaction. The stability is also made possible by a new dielectricmodel that is smooth both over time and over space, an important issue in the application of implicit solvents. In addition, the electrostatic focusing technique facilitates the use of an accurate yet efficient nonperiodic boundary condition: boundary grid potentials computed by the sum of potentials from individual grid charges. Finally, the particle–particle particle–mesh technique is adopted in the computation of the Coulombic interaction to balance accuracy and efficiency in simulations of large biomolecules. Preliminary testing shows that the nonperiodic Poisson–Boltzmann dynamics method is numerically stable in trajectories at least 4 ns long. The new model is also fairly efficient: it is comparable to that of the pairwise generalized Born solventmodel, making it a strong candidate for dynamics simulations of biomolecules in dilute aqueous solutions. Note that the current treatment of total electrostaticinteractions is with no cutoff, which is important for simulations of biomolecules. Rigorous treatment of the Debye–Huckel screening is also possible within the Poisson–Boltzmann framework: its importance is demonstrated by a simulation of a highly charged protein.
172 citations
TL;DR: In this article, analytical solutions for the effect of squeeze film damping on a MEMS torsion mirror were derived under the assumption of small displacements, and the damping torques based on both the analytical modeling and the numerical modeling were then used in the equation of motion of the torsions mirror which is solved by the Runge-Kutta numerical method.
Abstract: This paper presents analytical solutions for the effect of squeeze film damping on a MEMS torsion mirror. Both the Fourier series solution and the double sine series solution are derived for the linearized Reynold equation which is obtained under the assumption of small displacements. Analytical formulae for the squeeze film pressure variation and the squeeze film damping torque on the torsion mirror are derived. They are functions of the rotation angle and the angular velocity of the mirror. On the other hand, to verify the analytical modeling, the implicit finite difference method is applied to solve the nonlinear isothermal Reynold equation, and thus numerically determine the squeeze film damping torque on the mirror. The damping torques based on both the analytical modeling and the numerical modeling are then used in the equation of motion of the torsion mirror which is solved by the Runge-Kutta numerical method. We find that the dynamic angular response of the mirror based on the analytical damping model matches very well with that based on the numerical damping model. We also perform experimental measurements and obtain results which are consistent with those obtained from the analytical and numerical damping models. Although the analytical damping model is derived under the assumption of harmonic response of the torsion mirror, it is shown that with the air spring effect neglected, this damping model is still valid for the case of nonharmonic response. The dependence of the damping torque on the ambient pressure is also considered and found to be insignificant in a certain regime of the ambient pressure. Finally, the convergence of the series solutions is discussed, and an approximate one term formula is presented for the squeeze film damping torque on the torsion mirror.
171 citations
TL;DR: In this article, the field region is discretised by triangular Finite-elements and the solution to the field problem is obtained by minimizing the energy functional with respect to each of the vertex values of the vector potential.
Abstract: Analysis of the eddy-currentproblem in magnetic structures by the method of Finite-elements is presented. The linear diffusion equation representing the appropriate energy functional is described. The field region is discretised by triangular Finite-elements and the solution to the field problem is obtained by minimizing the energy functional with respect to each of the vertex values of the vector potential. Expressions for the magnetic field, electric field and eddy-current losses are presented. The method is applied to a few cases of engineering interest and compared with results of classical analysis and tests.
171 citations
TL;DR: In this article, a finite-difference method is presented for solving three-dimensional transient heat conduction problems, which achieves the higher-order accuracy of a Crank-Nicholson formulation while preserving the advantages of the Douglas-Rachford method.
Abstract: A finite-difference method is presented for solving three-dimensional transient heat conduction problems. The method is a modification of the method of Douglas and Rachford which achieves the higher-order accuracy of a Crank-Nicholson formulation while preserving the advantages of the Douglas-Rachford method: unconditional stability and simplicity of solving the equations at each time level. Although the method has not yet been applied, the analysis in this paper suggests that it will prove to be the most efficient method yet proposed for the numerical integration of three-dimensional transient heat conduction problems.
171 citations
TL;DR: A systematic procedure based on nonlocal approximation is proposed for the construction of qualitatively stable nonstandard finite difference schemes for the logistic equation, the combustion model and the reaction-diffusion equation.
170 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 53 |
| 2024 | 136 |
| 2023 | 170 |
| 2022 | 357 |
| 2021 | 733 |
| 2020 | 690 |