Related papers: High order volume-preserving algorithms for relati…
We introduce a second-order numerical scheme for compressible atmospheric motions at small to planetary scales. The collocated finite volume method treats the advection of mass, momentum, and mass-weighted potential temperature in…
Higher-order numerical methods are used to find accurate numerical solutions to hyperbolic partial differential equations and equations of transport type. Limiting is required to either converge to the correct type of solution or to adhere…
High-order spatial discretisations and full discretisations of parabolic partial differential equations on evolving surfaces are studied. We prove convergence of the high-order evolving surface finite element method, by showing high-order…
The primary challenge in solving kinetic equations, such as the Vlasov equation, is the high-dimensional phase space. In this context, dynamical low-rank approximations have emerged as a promising way to reduce the high computational cost…
We develop a quadratic regularization approach for the solution of high-dimensional multistage stochastic optimization problems characterized by a potentially large number of time periods/stages (e.g. hundreds), a high-dimensional resource…
This article provides a reduced-order modelling framework for turbulent compressible flows discretized by the use of finite volume approaches. The basic idea behind this work is the construction of a reduced-order model capable of providing…
We present an amelioration of current known algorithms for optimal spectral partitioning problems. The idea is to use the advantage of a representation using density functions while decreasing the computational time. This is done by…
We present a numerical scheme for the solution of a class of atmospheric models where high horizontal resolution is required while a coarser vertical structure is allowed. The proposed scheme considers a layering procedure for the original…
In this paper, we investigate the application of the maximum principle preserving (MPP) parametrized flux limiters to the high order finite volume scheme with Runge-Kutta time discretization for solving convection dominated problems. Such…
Centered finite volume methods are considered in the context of Numerical Relativity. A specific formulation is presented, in which third-order space accuracy is reached by using a piecewise-linear reconstruction. This formulation can be…
In this paper, we introduce and analyze a class of numerical schemes that demonstrate remarkable superiority in terms of efficiency, the preservation of positivity, energy stability, and high-order precision to solve the time-dependent…
Considering the use of dynamical systems in practical applications, often only limited regions in the time or frequency domain are of interest. Therefor, it usually pays off to compute local approximations of the used dynamical systems in…
In this paper we study the performance of a symplectic numerical integrator based on the splitting method. This method is applied to a subtle problem i.e. higher order resonance of the elastic pendulum. In order to numerically study the…
In this study, a new framework of constructing very high order discontinuity-capturing schemes is proposed for finite volume method. These schemes, so-called $\mathrm{P}_{n}\mathrm{T}_{m}-\mathrm{BVD}$ (polynomial of $n$-degree and THINC…
We present a conservative/dissipative time integration scheme for nonlinear mechanical systems. Starting from a weak form, we derive algorithmic forces and velocities that guarantee the desired conservation/dissipation properties. Our…
We present an adaptive-order positivity-preserving conservative finite-difference scheme that allows a high-order solution away from shocks and discontinuities while guaranteeing positivity and robustness at discontinuities. This is…
A novel hybrid spectral difference/embedded finite volume method is introduced in order to apply a discontinuous high-order method for large scale engineering applications involving discontinuities in the flows with complex geometries. In…
We propose and study a novel efficient algorithm for clustering and classification tasks based on the famous MBO scheme. On the one hand, inspired by Jacobs et al. [J. Comp. Phys. 2018], we introduce constraints on the size of clusters…
We present a splitting-free variant of the vorticity redistribution method. Spatial consistency and stability when combined with a time-stepping scheme are proven. We propose a new strategy preventing excessive growth in the number of…
The scalar wave equation is solved using higher order immersed finite elements. We demonstrate that higher order convergence can be obtained. Small cuts with the background mesh are stabilized by adding penalty terms to the weak…