Related papers: A sixth order averaged vector field method
We present a uniform approach to the construction of the groups of type $\mathrm{E}_6$ over arbitrary fields without using Lie theory. This gives a simple description of the group generators and some of the subgroup structure. In the finite…
This paper compares two actuator line methodologies for modelling wind turbines employing high-order h/p solvers and large-eddy simulations. The methods combine the accuracy of high-order solvers (in this work the maximum order is 6) with…
An AVL tree is the original type of balanced binary search tree. An insertion in an $n$-node AVL tree takes at most two rotations, but a deletion in an $n$-node AVL tree can take $\Theta(\log n)$. A natural question is whether deletions can…
$K^2 S^2 T [5]$ recently derived a new 6$^{th}$-order wave equation $KdV6$: $(\partial^2_x + 8u_x \partial_x + 4u_{xx})(u_t + u_{xxx} + 6u_x^2) = 0$, found a linear problem and an auto-B${\ddot{\rm{a}}}$ckclund transformation for it, and…
We study whether iterated vector fields (vector fields composed with themselves) are conservative. We give explicit examples of vector fields for which this self-composition preserves conservatism. Notably, this includes gradient vector…
Burger et al.in \cite{karlsen-1} proposed a flux TVD (FTVD) second order scheme by using a new non local limiter algorithm for conservation laws with discontinuous flux modeling clarifier thickener units. In this work we show that their…
Continual learning based on data stream mining deals with ubiquitous sources of Big Data arriving at high-velocity and in real-time. Adaptive Random Forest ({\em ARF}) is a popular ensemble method used for continual learning due to its…
We present an new system of ordinary differential equations with affine Weyl group symmetry of type E_6^{(1)}. This system is expressed as a Hamiltonian system of sixth order with a coupled Painleve VI Hamiltonian.
The construction of a family of real Hamiltonian forms (RHF) for the special class of affine 1+1-dimensional Toda field theories (ATFT) is reported. Thus the method, proposed in [1] for systems with finite number of degrees of freedom is…
Though sufficient for local conservation of charge, Maxwells displacement current is not necessary. An alternative to the Ampere-Maxwell equation is exhibited and the alternatives electric and magnetic fields and scalar and vector…
Variational Quantum Algorithms (VQAs) are critically threatened by the Barren Plateau (BP) phenomenon. In this work, we introduce the H-EFT Variational Ansatz (H-EFT-VA), an architecture inspired by Effective Field Theory (EFT). By…
In this paper, we develop a high-order adaptive virtual element method (VEM) to simulate the self-consistent field theory (SCFT) model in arbitrary domains. The VEM is very flexible in handling general polygon elements and can treat hanging…
The active flux (AF) method is a compact high-order finite volume method that evolves cell averages and point values at cell interfaces independently. Within the method of lines framework, the point value can be updated based on Jacobian…
For Hamiltonian systems with non-canonical structure matrices, a new family of fourth-order energy-preserving integrators is presented. The integrators take a form of a combination of Runge--Kutta methods and continuous-stage Runge--Kutta…
In recent years, dynamically growing data and incrementally growing number of classes pose new challenges to large-scale data classification research. Most traditional methods struggle to balance the precision and computational burden when…
The consistent recursive subtraction of UV divergences order by order in the loop expansion for spontaneously broken effective field theories with dimension-6 derivative operators is presented for an Abelian gauge group. We solve the…
We present a family of multistep integrators based on the Adams-Bashforth methods. These schemes can be constructed for arbitrary convergence order with arbitrary step size variation. The step size can differ between different subdomains of…
This paper proposes a new class of arbitrarily high-order conservative numerical schemes for the generalized Korteweg-de Vries (KdV) equation. This approach is based on the scalar auxiliary variable (SAV) method. The equation is…
The goal of this paper is to develop energy-preserving variational integrators for time-dependent mechanical systems with forcing. We first present the Lagrange-d'Alembert principle in the extended Lagrangian mechanics framework and derive…
A Block Structure Preserving Model Order Reduction approach is proposed for Integral Equations methods based on the Augmented Electric Field Integral Equation. This approach allows for representing the unknown fields with dedicated…