相关论文: Invariant grids for reaction kinetics

Motivation: A Chemical Reaction Network (CRN) is a set of chemical reactions, which can be very complex and difficult to analyze. Indeed, dynamical properties of CRNs can be described by a set of non-linear differential equations that…

Advancements in computational fluid mechanics have largely relied on Newtonian frameworks, particularly through the direct simulation of Navier-Stokes equations. In this work, we propose an alternative computational framework that employs…

This paper investigates model-order reduction methods for geometrically nonlinear structures. The parametrisation method of invariant manifolds is used and adapted to the case of mechanical systems expressed in the physical basis, so that…

The Truncated Nonsmooth Newton Multigrid (TNNMG) method is a robust and efficient solution method for a wide range of block-separable convex minimization problems, typically stemming from discretizations of nonlinear and nonsmooth partial…

We consider discrete Poisson interface problems resulting from linear unfitted finite elements, also called cut finite elements (CutFEM). Three of these unfitted finite element methods known from the literature are studied. All three…

Estimating rate coefficients from complex chemical reactions is essential for advancing detailed chemistry. However, the stiffness inherent in real-world atmospheric chemistry systems poses severe challenges, leading to training instability…

To solve MHD problems within the framework of the theory of two-scale mean fields, it is important to study the invariants of magnetic lines. Such invariants are constructed on the basis of invariants of classical links, which must satisfy…

We present a numerical method for solving the Poisson equation on a nested grid. The nested grid consists of uniform grids having different grid spacing and is designed to cover the space closer to the center with a finer grid. Thus our…

We define a subclass of Chemical Reaction Networks called Post-Translational Modification systems. Important biological examples of such systems include MAPK cascades and two-component systems which are well-studied experimentally as well…

Manifold-based combustion models decrease the cost of turbulent combustion simulations by projecting the thermochemical state onto a lower-dimensional manifold, allowing the thermochemical state to be computed separately from the flow…

The minimum action method (MAM) is to calculate the most probable transition path in randomly perturbed stochastic dynamics, based on the idea of action minimization in the path space. The accuracy of the numerical path between different…

We here introduce a novel scheme for generating smoothly-varying infill graded microstructural (IGM) configurations from a given menu of generating cells. The scheme was originally proposed for essentially improving the variety of…

Based on previous work we extend a primal-dual semi-smooth Newton method for minimizing a general $L^1$-$L^2$-$TV$ functional over the space of functions of bounded variations by adaptivity in a finite element setting. For automatically…

We introduce an algorithm to solve linear inverse problems regularized with the total (gradient) variation in a gridless manner. Contrary to most existing methods, that produce an approximate solution which is piecewise constant on a fixed…

In Gander et al. [2004] we proposed a new non-conforming domain decomposition paradigm, the New Interface Cement Equilibrated Mortar (NICEM) method, based on Schwarz type methods that allows for the use of Robin interface conditions on…

The Asymptotic Iteration Method (AIM) is a technique for solving analytically and approximately the linear second-order differential equation, especially the eigenvalue problems that frequently appear in theoretical and mathematical…

Invariant manifolds facilitate the understanding of nonlinear stochastic dynamics. When an invariant manifold is represented approximately by a graph for example, the whole stochastic dynamical system may be reduced or restricted to this…

Iterative methods are widely used for solving partial differential equations (PDEs). However, the difficulty in eliminating global low-frequency errors significantly limits their convergence speed. In recent years, neural networks have…

We present a polynomial multigrid method for the nodal interior penalty formulation of the Poisson equation on three-dimensional Cartesian grids. Its key ingredient is a weighted overlapping Schwarz smoother operating on element-centered…

Cartan's method of moving frames is briefly recalled in the context of immersed curves in the homogeneous space of a Lie group $G$. The contact geometry of curves in low dimensional equi-affine geometry is then made explicit. This delivers…