Journal of Computational Physics

We present an efficient and accurate energy-conserving implicit particle-in-cell (PIC) algorithm for the electrostatic Vlasov system, with particular emphasis on its high robustness for simulating complex plasma systems with multiple physical ...

In this paper, we propose a finite element method for solving the coupled model of classical drift-diffusion equations and Schrödinger-Poisson equations in simulating a resonant tunneling diode (RTD). The coupling coefficient Θ and the quantum ...

• We first prove a growth rate of | ψ p | as | p | → + ∞. Based on this, the momentum space can be truncated to a bounded interval.
• We propose an adaptive algorithm which adjusts the partition of the momentum domain based on a posteriori ...

A novel staggered semi-implicit finite volume method for the simulation of one-dimensional blood flow in networks of elastic and viscoelastic vessels is proposed. The one-dimensional blood flow model is split into three subsystems: one containing ...

• Novel semi-implicit finite volume method for blood flow in networks of compliant vessels.
• Tube law for arteries and veins accounting also for visco-elastic effects.
• Splitting of the PDE into a convective, a viscous and a pressure ...

We consider the approximation of a class of dynamic partial differential equations (PDEs) of second order in time by the physics-informed neural network (PINN) approach, and provide an error analysis of PINN for the wave equation, the nonlinear ...

In this article, we propose a data-driven reduced basis (RB) method for the approximation of parametric eigenvalue problems. The method is based on the offline and online paradigms. In the offline stage, we generate snapshots and construct the ...

• In this article, we propose a data-driven reduced basis (RB) method for the approximation of parametric eigenvalue problems. The method is based on the offline and online paradigms.
• In the offline stage, we generate snapshots and ...

High-order implicit shock tracking (fitting) is a class of high-order, optimization-based numerical methods to approximate solutions of conservation laws with non-smooth features by aligning elements of the computational mesh with non-smooth ...

• Robust many-query analysis of flow problems with parametrized lead shock.
• Parameter-dependent lead shock treated as moving boundary.
• Moving shock boundary determined using implicit shock tracking.
• Elements upstream of lead ...

The ALLIANCE (ALLIANCE - spectrAL soLver for kInetic plAsma turbuleNCE) code is developed to solve a new set of four-dimensional electromagnetic drift-kinetic equations in slab geometry [1]. The nonlinear equations are useful for the study of ...

• Four-dimensional equations to study plasma turbulence are presented in the form applicable for numerical studies.
• Numerical tests proving convergence of linear and nonlinear solver are shown.
• Linear run showing the linear phase ...

In this work, we tackle the problem of minimising the Conditional-Value-at-Risk (CVaR) of output quantities of complex differential models with random input data, using gradient-based approaches in combination with the Multi-Level Monte Carlo (...

• Conditional-Value-at-Risk (CvaR) sensitivities using Parametric Expectations (PE).
• Estimating sensitivities using Multi-Level Monte Carlo (MLMC) for PE.
• Alternating minimization gradient-descent algorithm using MLMC sensitivities.

This work introduces meta estimators that combine multiple multifidelity techniques based on control variates, importance sampling, and information reuse to yield a quasi-multiplicative amount of variance reduction. The proposed meta estimators ...

• Meta variance reduction combining control variates, importance sampling, and information reuse.
• Quasi-multiplicative amount of variance reduction compared to constituent methods.
• Orders of magnitude speedup compared to standard ...

Complex nonlinear partial differential equations (PDEs) can be decomposed into subsystems comprising certain linear and nonlinear sub-operators. We usually have fundamental solutions to the linear subsystems and have a good knowledge of their ...

• A proper subsystem decomposition of the nonlinear PDEs to get unique solutions is derived.
• The SONets based on proper subsystem decomposition to solve nonlinear PDEs are proposed.
• It is convenient to generalize SONets for a new PDE ...

In a recent article the authors showed that the radiative Transfer equations with multiple frequencies and scattering can be formulated as a nonlinear integral system. In the present article, the formulation is extended to handle reflective ...

• We present a method and a an algorithm using an H-matrix compression scheme to compute the temperature of a gas under electromagnetic radiations.
• The method is now capable of handling reflective boundaries.
• The paper improves on ...

The goal of this work is to address two limitations in autoencoder-based models: latent space interpretability and compatibility with unstructured meshes. This is accomplished here with the development of a novel graph neural network (GNN) ...

• A graph neural network autoencoder is developed for latent space interpretability.
• Latent graphs can be accessed as time-evolving coherent structures in physical space.
• Multi-scale message passing layers are employed to improve ...

In this paper, we develop a maximum principle preserving Monte Carlo method for the frequency-dependent (multi-group) radiative transfer equations. In order to deal with the nonlinear coupling between the radiation intensity and background ...

• A new iterative implicit Monte Carlo method is derived based on the Newton's iteration for frequency-dependent TRT equations.
• The new method becomes a fully implicit discretization of the multi-group TRT equations if convergence can be ...

In this paper, we propose a novel interior penalty discontinuous Galerkin projection method for the incompressible magneto-hydrodynamic equations. The scheme is employed by an implicit-explicit treatment of the nonlinear coupling terms and a ...

• A novel interior penalty discontinuous Galerkin projection scheme for the MHD system is developed.
• The scheme is linear, fully-decoupled, second-order in time and unconditional energy stable.
• The well-posedness and energy stability ...

Based on generalized porous flow model, we present a one-domain framework for the simulation of incompressible flow in superposed clear and porous media. The continuous change in the characteristics of the porous medium is naturally taken into ...

A finite difference scheme is used to develop a numerical method to solve the flow of an unbounded viscoelastic fluid with zero to moderate inertia around a prolate spheroidal particle. The equations are written in prolate spheroidal coordinates, ...

• A finite difference method for viscoelasticity and moderate inertia around spheroids.
• Prolate spheroidal coordinates efficiently resolve particle surface and large gradients.
• L'Hopital rule eliminates coordinate system generated ...

This article deals with the optimization of resonant plasmonic metasurfaces through their surface-homogenized counterpart. The derivation of effective transition conditions that takes into account the spatially varying geometries is done using ...

• Effective transition conditions for quasi-periodic metasurfaces with plasmonic resonances are derived.
• We adapt the bulk homogenization-based optimization method to surface-homogenized metasurfaces.
• Examples showing the versatility ...

A generalized variational level set method without frequent reinitialization process is proposed to address the issue of the traditional level set method for detailed numerical simulations of gas-liquid flows. The gas-liquid interface is captured ...

• A generalized variational level set method without frequent reinitialization process is proposed to simulate gas-liquid flows.
• A penalty term is added in the classical level set advection equation to reduce the frequent ...

Frequency-domain wave scattering problems that arise in acoustics and electromagnetism can be often described by the Helmholtz equation. This work presents a boundary integral equation method for the Helmholtz equation in 3-D multilayered media ...

• Boundary integral equation method and periodizing scheme for the Helmholtz equation in 3-D multilayered media.
• High-order surface quadrature rule based on an error-corrected Trapezoidal quadrature method.
• Linear growth of ...

We propose a new framework for the design of fast-projection solvers for the Navier-Stokes equations using Runge-Kutta integrators. The framework uses the full nonlinear equations along with rooted trees and exposes the need to track non-linear ...

• A new nonlinear framework to develop fast projection methods using rooted trees.
• New fully parametric fast projection integrators for RK3, and RK4.
• New fast projection schemes with adaptive timestepping.
• New rooted trees for ...

Solid and fluid mechanics problems often involve the computation of eigenvalues and eigenvectors. One has short algebraic expressions for the Euler equations and the perfect gas equation of state. However, algebraic expressions for solid ...

• We proposed and tested approximated decompositions for computational continuum mechanics.
• The approximated decompositions are more flexible but more expensive.
• The approximated eigensystem decomposition is high-order and high-...

This paper continues to study linear and unconditionally modified-energy stable (abbreviated as SAV-GL) schemes for the gradient flows. The schemes are built on the SAV technique and the general linear time discretizations (GLTD) as well as the ...

High-fidelity computation of shock-associated noise places stringent requirements on the accuracy, linear and nonlinear spectral properties of shock-capturing scheme. In this paper, a novel weighted nonlinear compact scheme with seventh-order ...

• A novel seventh-order weighted compact scheme named WCOM7S is proposed.
• WCOM7S reduces the dissipation and dispersion at medium and high wavenumbers.
• WCOM7S has good nonlinear spectral properties and weak nonlinear effect.

This paper proposes a topology optimization procedure to reconstruct sharp interfaces of salt bodies in a background medium with known properties. The reconstruction technique uses the time-domain acoustic wave equation that provides the pressure ...

• Procedure to reconstruct sharp interfaces using a level set approach and cut elements.
• Acoustic full-waveform inversion in the time domain 3.
• A level set-cut element approach provides accurate solutions to the problem.
• ...