Related papers: High-order WENO scheme for Polymerization-type equ…
This paper develops high-order accurate, well-balanced (WB), and positivity-preserving (PP) finite volume schemes for shallow water equations on adaptive moving structured meshes. The mesh movement poses new challenges in maintaining the WB…
We present a class of high order finite volume schemes for the solution of non-conservative hyperbolic systems that combines the one-step ADER-WENO finite volume approach with space-time adaptive mesh refinement (AMR). The resulting…
Feature matters. How to train a deep network to acquire discriminative features across categories and polymerized features within classes has always been at the core of many computer vision tasks, specially for large-scale recognition…
We present a newly developed cosmological hydrodynamics code based on weighted essentially non-oscillatory (WENO) schemes for hyperbolic conservation laws. WENO is a higher order accurate finite difference scheme designed for problems with…
In this work, we present a family of time and space high order finite volume schemes for the solution of the full Boltzmann equation. The velocity space is approximated by using a discrete ordinate approach while the collisional integral is…
We devise and evaluate numerically a Hybrid High-Order (HHO) method for finite plasticity within a logarithmic strain framework. The HHO method uses as discrete unknowns piecewise polynomials of order $k\ge1$ on the mesh skeleton, together…
The goal of the present paper is to understand the impact of numerical schemes for the reconstruction of data at cell faces in finite-volume methods, and to assess their interaction with the quadrature rule used to compute the average over…
We present a new version of conservative ADER-WENO finite volume schemes, in which both the high order spatial reconstruction as well as the time evolution of the reconstruction polynomials in the local space-time predictor stage are…
This paper concerns the construction and analysis of a numerical scheme for a mixed discrete-continuous fragmentation equation. A finite volume scheme is developed, based on a conservative formulation of a truncated version of the…
A new adaptive weighted essentially non-oscillatory WENO-$\theta$ scheme in the context of finite difference is proposed. Depending on the smoothness of the large stencil used in the reconstruction of the numerical flux, a parameter…
In this paper, we utilize the maximum-principle-preserving flux limiting technique, originally designed for high order weighted essentially non-oscillatory (WENO) methods for scalar hyperbolic conservation laws, to develop a class of high…
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…
Proteins are a matter of dual nature. As a physical object, a protein molecule is a folded chain of amino acids with multifarious biochemistry. But it is also an instantiation along an evolutionary trajectory determined by the function…
We describe the results obtained from an improved model for protein folding. We find that a good agreement with the native structure of a 46 residue long, five-letter protein segment is obtained by carefully tuning the parameters of the…
We present a number of new contributions to the topic of constructing efficient higher-order splitting methods for the numerical integration of evolution equations. Particular schemes are constructed via setup and solution of polynomial…
Polynomial dynamical systems are widely used to model and study real phenomena. In biochemistry, they are the preferred choice for modelling the concentration of chemical species in reaction networks with mass-action kinetics. These systems…
The protein design problem involves finding polypeptide sequences folding into a given threedimensional structure. Its rigorous algorithmic solution is computationally demanding, involving a nested search in sequence and structure spaces.…
When constructing high-order schemes for solving hyperbolic conservation laws, the corresponding high-order reconstructions are commonly performed in characteristic spaces to eliminate spurious oscillations as much as possible. For…
In this paper, high order semi-implicit well-balanced and asymptotic preserving finite difference WENO schemes are proposed for the shallow water equations with a non-flat bottom topography. We consider the Froude number ranging from O(1)…
In this paper, a higher order finite difference scheme is proposed for Generalized Fractional Diffusion Equations (GFDEs). The fractional diffusion equation is considered in terms of the generalized fractional derivatives (GFDs) which uses…