Related papers: Dynamic Implicit 3D Adaptive Mesh Refinement for N…
We consider locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of parabolic initial-boundary value problems with variable, possibly discontinuous in space…
Implicit Neural Representations (INRs) are a learning-based approach to accelerate Magnetic Resonance Imaging (MRI) acquisitions, particularly in scan-specific settings when only data from the under-sampled scan itself are available.…
Similarity solutions to the nonlinear non-equilibrium Marshak wave problem with a time dependent radiation driving source are presented. The radiation transfer model used is the gray, non-equilibrium diffusion approximation in the…
We present a novel energy-based numerical analysis of semilinear diffusion-reaction boundary value problems. Based on a suitable variational setting, the proposed computational scheme can be seen as an energy minimisation approach. More…
We present a modification to the Berger and Oliger adaptive mesh refinement algorithm designed to solve systems of coupled, non-linear, hyperbolic and elliptic partial differential equations. Such systems typically arise during constrained…
The paper investigates a non-intrusive parallel time integration with multigrid for space-fractional diffusion equations in two spatial dimensions. We firstly obtain a fully discrete scheme via using the linear finite element method to…
Non-equilibrium radiation diffusion is an important mechanism of energy transport in Inertial Confinement Fusion, astrophysical plasmas, furnaces and heat exchangers. In this paper, an analytical solution to the non-equilibrium Marshak…
An adaptive mesh refinement (AMR) scheme is implemented in a distributed environment using Message Passing Interface (MPI) to find solutions to the nonlinear sigma model. Previous work studied behavior similar to black hole critical…
A method is developed for solving quasilinear convection diffusion problems starting on a coarse mesh where the data and solution-dependent coefficients are unresolved, the problem is unstable and approximation properties do not hold. The…
We have implemented non-ideal Magneto-Hydrodynamics (MHD) effects in the Adaptive Mesh Refinement (AMR) code RAMSES, namely ambipolar diffusion and Ohmic dissipation, as additional source terms in the ideal MHD equations. We describe in…
An implicit method for the ohmic dissipation is proposed. The proposed method is based on the Crank-Nicolson method and exhibits second-order accuracy in time and space. The proposed method has been implemented in the SFUMATO adaptive mesh…
Adaptive mesh refinement (AMR) is often used when solving time-dependent partial differential equations using numerical methods. It enables time-varying regions of much higher resolution, which can be used to track discontinuities in the…
Mesh generation is essential for accurate and efficient computational fluid dynamics simulations. To resolve critical features in the flow, adaptive mesh refinement (AMR) is routinely employed in certain regions of the computational domain,…
Magnetic Resonance Imaging (MRI) is a widely applied non-invasive imaging modality based on non-ionizing radiation which gives excellent images and soft tissue contrast of living tissues. We consider the modified Bloch problem as a model of…
We describe an application of Berger and Colella's structured adaptive mesh refinement algorithm to the field of cosmological astrophysics. Simulations in this area must include not just a gaseous component which follows the hyperbolic…
This work presents a high-order finite-difference adaptive mesh refinement (AMR) framework for robust simulation of shock-turbulence interaction problems. A staggered-grid arrangement, in which solution points are stored at cell centers…
For reaction-diffusion equations in irregular domain with moving boundaries, the numerical stability constraints from the reaction and diffusion terms often require very restricted time step size, while complex geometries may lead to…
When numerically solving partial differential equations, for a given problem and operating condition, adaptive mesh refinement (AMR) has proven its efficiency to automatically build a discretization achieving a prescribed accuracy at low…
This article initiates the study of space-time adaptive mesh refinements for time-dependent boundary element formulations of wave equations. Based on error indicators of residual type, we formulate an adaptive boundary element procedure for…
We describe a powerful methodology for numerical solution of 3-D self-gravitational hydrodynamics problems with extremely high resolution. Our method utilizes the technique of local adaptive mesh refinement (AMR), employing multiple grids…