Related papers: Improved Nonlinear Solvers in BOUT++
We study efficient simulation of steady state for rarefied gas flow, which is modeled by the Boltzmann equation with BGK-type collision term. A nonlinear multigrid solver is proposed to resolve the efficiency issue by the following…
The paper focuses on developing and studying efficient block preconditioners based on classical algebraic multigrid for the large-scale sparse linear systems arising from the fully coupled and implicitly cell-centered finite volume…
Linear systems in applications are typically well-posed, and yet the coefficient matrices may be nearly singular in that the condition number $\kappa(\boldsymbol{A})$ may be close to $1/\varepsilon_{w}$, where $\varepsilon_{w}$ denotes the…
We consider the numerical solution of time-dependent space tempered fractional diffusion equations. The use of Crank-Nicolson in time and of second-order accurate tempered weighted and shifted Gr\"unwald difference in space leads to dense…
We develop a fully-coupled, fully-implicit approach for phase-field modeling of solidification in metals and alloys. Predictive simulation of solidification in pure metals and metal alloys remains a significant challenge in the field of…
The method of using neural networks (NNs) for turbulent transport prediction in a simplified model of tokamak plasmas is explored. The NNs are trained on a database obtained via test-particle simulations of a transport model in the…
Solving systems of linear equations is a problem occuring frequently in water engineering applications. Usually the size of the problem is too large to be solved via direct factorization. One can resort to iterative approaches, in…
A mathematical model for the charging simulation of non-insulated superconducting pancake solenoids is presented. Numerical solutions are obtained by the simulation model implemented on the Petra-M FEM platform using a variety of solvers. A…
A challenging and fundamental research problem is the better understanding and control of the turbulent transport of heat in present-day tokamak fusion experiments. Recent developments in numerical methods along with enormous gains in…
This paper explores the feasibility of quantum simulation for partial differential equations (PDEs) with physical boundary or interface conditions. Semi-discretisation of such problems does not necessarily yield Hamiltonian dynamics and…
Uncertainty quantification (UQ) tasks, such as sensitivity analysis and parameter estimation, entail a huge computational complexity when dealing with input-output maps involving the solution of nonlinear differential problems, because of…
The properties of the boundary plasma in a tokamak are now recognized to play a key role in determining the achievable fusion power and the lifetimes of plasma-facing components. Accurate quantitative modeling and improved qualitative…
This paper describes an efficient and nonlinearly consistent parallel solution methodology for solving coupled nonlinear thermal transport problems that occur in nuclear reactor applications over hundreds of individual 3D physical…
Fast and stable fluid simulations are an essential prerequisite for applications ranging from computer-generated imagery to computer-aided design in research and development. However, solving the partial differential equations of…
The electromagnetic behavior of plasmonic structures can be predicted after discretizing and solving a linear system of equations, derived from a continuous surface integral equation (SIE) and the appropriate boundary conditions, using a…
In this note we present a multigrid preconditioning method for solving quadratic optimization problems constrained by a fractional diffusion equation. Multigrid methods within the all-at-once approach to solve the first order-order…
We present a compatible finite element discretisation for the vertical slice compressible Euler equations, at next-to-lowest order (i.e., the pressure space is bilinear discontinuous functions). The equations are numerically integrated in…
Modeling cardiovascular blood flow is central to many applications in biomedical engineering. To accommodate the complexity of the cardiovascular system, in terms of boundary conditions and surrounding vascular tissue, computational fluid…
For some typical and widely used non-convex half-quadratic regularization models and the Ambrosio-Tortorelli approximate Mumford-Shah model, based on the Kurdyka-\L ojasiewicz analysis and the recent nonconvex proximal algorithms, we…
Accurate and rapid simulation of the free boundary tokamak plasma equilibrium evolution is essential for modern plasma control, stability analysis, and scenario development. This paper presents the Free-Boundary Grad-Shafranov Evolutive…