相关论文: Taylor States in Stellarators: A Fast High-order B…

This work focuses on the preconditioning and DC stabilization of the time domain electric field integral equation discretized in time with the convolution quadrature method. The standard formulation of the equation suffers from severe…

In our previous work [SIAM J. Sci. Comput. 43(3) (2021) B784-B810], an accurate hyper-singular boundary integral equation method for dynamic poroelasticity in two dimensions has been developed. This work is devoted to studying the more…

In this paper we describe a method to compute Generalized Polarization Tensors. These tensors are the coefficients appearing in the multipolar expansion of the steady state voltage perturbation caused by an inhomogeneity of constant…

This paper deals with iteration stable (STIT) tessellations, and, more generally, with a certain class of tessellations that are infinitely divisible with respect to iteration. They form a new, rich and flexible class of spatio-temporal…

A stable volume integral equation (VIE) solver based on polarization/magnetization currents is presented, for the accurate and efficient computation of the electromagnetic scattering from highly inhomogeneous and high contrast objects.We…

We introduce a novel approach for the simultaneous optimization of plasma physics and coil engineering objectives using fixed-boundary equilibria that is computationally efficient and applicable to a broad range of vacuum and finite plasma…

Building upon recent results obtained in [7,8,9], we describe an efficient second order, A-stable scheme for solving the wave equation, based on the method of lines transpose (MOL$^T$), and the resulting semi-discrete (i.e. continuous in…

Good magnetic surfaces, as opposed to magnetic islands and chaotic field lines, are generally desirable for stellarators. In previous work, M. Landreman et al. [Phys. of Plasmas 28, 092505 (2021)] showed that equilibria computed by the…

Numerical computation of the ideal Magnetohydrodynamic (MHD) equilibrium magnetic field is at the base of stellarator optimisation and provides the starting point for solving more sophisticated Partial Differential Equations (PDEs) like…

The problem of finding an optimal curve for the target magnetic axis of a stellarator is addressed. Euler-Lagrange equations are derived for finite length three-dimensional curves that extremise their bending energy while yielding fixed…

Inspired by the design for the simple Columbia Non-neutral Torus (CNT) proposed by Pedersen and Boozer (Phys. Rev. Lett. 88 205002(2002)), and later revisited by Yu et al. (J. Plasma Phys. 88 905880306 (2022)), this work explores…

A hierarchical solver is proposed for solving sparse ill-conditioned linear systems in parallel. The solver is based on a modification of the LoRaSp method, but employs a deferred-compression technique, which provably reduces the…

In this work we consider the problem of optimizing a stellarator subject to hard constraints on the design variables and physics properties of the equilibrium. We survey current numerical methods for handling these constraints, and…

This paper demonstrates new methods and implementations of nonlinear solvers with higher-order of convergence, which is achieved by efficiently computing higher-order derivatives. Instead of computing full derivatives, which could be…

We present an efficient and flexible method for solving the non-linear lasing equations of the steady-state ab initio laser theory. Our strategy is to solve the underlying system of partial differential equations directly, without the need…

Discrete regularization methods are often applied for obtaining stable approximate solutions for ill-posed operator equations $Tx=y$, where $T: X\to Y$ is a bounded operator between Hilbert spaces with non-closed range $R(T)$ and $y\in…

An unconventional approach is applied to solve the one-dimensional Burgers' equation. It is based on spline polynomial interpolations and Hopf-Cole transformation. Taylor expansion is used to approximate the exponential term in the…

We present a Calder\'on preconditioner for the electric field integral equation (EFIE), which does not require a barycentric refinement of the mesh and which yields a Hermitian, positive definite (HPD) system matrix allowing for the usage…

This paper proposes a collocation boundary element method based on the Burton--Miller method for solving transmission problems, which is rapidly convergent within the Krylov subspace solver framework. Our study enhances Burton--Miller-type…

In this paper, we introduce a fast Fourier-Galerkin method for solving boundary integral equations on torus-shaped surfaces, which are diffeomorphic to a torus. We analyze the properties of the integral operator's kernel to derive the decay…