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In this paper a mixed spectral element formulation is presented for planar, linear elasticity. The degrees of freedom for the stress are integrated traction components, i.e. surface force components. As a result the tractions between…

Numerical Analysis · Mathematics 2018-03-06 K. Olesen , B. Gervang , J. N. Reddy , M. Gerritsma

The Poisson equation governing a planet's gravitational field is posed on the unbounded domain, $\mathbb{R}^3$, whereas finite-element computations require bounded meshes. We implement and compare three strategies for handling the infinite…

Earth and Planetary Astrophysics · Physics 2026-02-13 Ziheng Yu , Alex D. C. Myhill , David Al-Attar

A novel boundary element formulation for solving problems involving eddy currents in the thin skin depth approximation is developed. It is assumed that the time-harmonic magnetic field outside the scatterers can be described using the…

Computational Physics · Physics 2021-02-03 Nail A. Gumerov , Ross N. Adelman , Ramani Duraiswami

In this paper, we develop an adaptive finite element method for the nonlinear steady-state Poisson-Nernst-Planck equations, where the spatial adaptivity for geometrical singularities and boundary layer effects are mainly considered. As a…

Numerical Analysis · Mathematics 2020-08-21 Tingting Hao , Manman Ma , Xuejun Xu

In Yang et al. [Nature 576, 248 (2019)], the authors introduced a general theoretical framework for nanoscale electromagnetism based on Feibelman parameters. Here quantum effects of the optically excited electrons at the interface between…

Mesoscale and Nanoscale Physics · Physics 2022-03-08 Ulrich Hohenester , Gerhard Unger

In contrast to the commonly used lattice Boltzmann method, off-lattice Boltzmann methods decouple the velocity discretization from the underlying spatial grid, thus allowing for more efficient geometric representations of complex…

The influence and validity of wall boundary conditions for non-equilibrium fluid flows described by the Boltzmann equation remains an open problem. The substantial computational cost of directly solving the Boltzmann equation has limited…

Fluid Dynamics · Physics 2024-01-02 Tarik Dzanic , Freddie D. Witherden , Luigi Martinelli

We describe a new, adaptive solver for the two-dimensional Poisson equation in complicated geometries. Using classical potential theory, we represent the solution as the sum of a volume potential and a double layer potential. Rather than…

Numerical Analysis · Mathematics 2022-11-29 Fredrik Fryklund , Leslie Greengard

The Immersed Boundary (IB) method of Peskin (J. Comput. Phys., 1977) is useful for problems involving fluid-structure interactions or complex geometries. By making use of a regular Cartesian grid that is independent of the geometry, the IB…

Numerical Analysis · Mathematics 2024-02-06 Brittany J. Leathers , Robert D. Guy

A modified Poisson-Nernst-Planck system in a bounded domain with mixed Dirichlet-Neumann boundary conditions is analyzed. It describes the concentrations of ions immersed in a polar solvent and the correlated electric potential due to the…

Analysis of PDEs · Mathematics 2023-05-25 Ansgar Jüngel , Annamaria Massimini

In this paper we develop a methodology for the mesoscale simulation of strong electrolytes. The methodology is an extension of the Fluctuating Immersed Boundary (FIB) approach that treats a solute as discrete Lagrangian particles that…

The interaction of screw dislocations with an applied stress is studied using atomistic simulations in conjunction with a continuum treatment of the role played by the far field boundary condition. A finite cell of atoms is used to consider…

Materials Science · Physics 2009-10-28 Vijay B. Shenoy , Rob Phillips

A Morley-Wang-Xu (MWX) element method with a simply modified right hand side is proposed for a fourth order elliptic singular perturbation problem, in which the discrete bilinear form is standard as usual nonconforming finite element…

Numerical Analysis · Mathematics 2020-12-01 Xuehai Huang , Yuling Shi , Wenqing Wang

Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted…

Numerical Analysis · Mathematics 2024-02-27 Jennifer E. Fromm , Nils Wunsch , Kurt Maute , John A. Evans , Jiun-Shyan Chen

We study the geometric particle-in-cell methods for an electrostatic hybrid plasma model. In this model, ions are described by the fully kinetic equations, electron density is determined by the Boltzmann relation, and space-charge effects…

Numerical Analysis · Mathematics 2026-03-26 Yingzhe Li

The immersed boundary-finite element method (IBFE) is an approach to describing the dynamics of an elastic structure immersed in an incompressible viscous fluid. In this formulation, there are discontinuities in the pressure and viscous…

Numerical Analysis · Mathematics 2020-03-18 Charles Puelz , Boyce E. Griffith

We consider in this paper random batch interacting particle methods for solving the Poisson-Nernst-Planck (PNP) equations, and thus the Poisson-Boltzmann (PB) equation as the equilibrium, in the external unbounded domain. To justify the…

Numerical Analysis · Mathematics 2022-03-25 Lei Li , Jian-Guo Liu , Yijia Tang

When dilute charged particles are confined in a bounded domain, boundary effects are crucial in the global dynamics. We construct a unique global-in-time solution to the Vlasov-Poisson-Boltzmann system in convex domains with the diffuse…

Analysis of PDEs · Mathematics 2019-04-08 Yunbai Cao , Chanwoo Kim , Donghyun Lee

The Poisson-Boltzmann equation (PBE) is an implicit solvent continuum model for calculating the electrostatic potential and energies of ionic solvated biomolecules. However, its numerical solution remains a significant challenge due strong…

Numerical Analysis · Mathematics 2023-06-13 Cleophas Kweyu , Venera Khoromskaia , Boris Khoromskij , Matthias Stein , Peter Benner

We revisit force evaluation methodologies on rigid solid particles suspended in a viscous fluid and simulated via lattice Boltzmann method (LBM). We point out the non-commutativity of streaming and collision operators in the force…

Fluid Dynamics · Physics 2022-10-20 Shaurya Kaushal , Sauro Succi , Santosh Ansumali