Related papers: Direct stellarator coil optimization for nested ma…
In this work, the problem of optimizing damper positions in vibrational systems is investigated. The objective is to determine the positions of external dampers in such a way that the influence of the input on the output is minimized. The…
This paper addresses the challenge of accommodating nonlinear dynamics and constraints in rapid trajectory optimization, envisioned for use in the context of onboard guidance. We present a novel framework that uniquely employs…
We show that in perfectly quasi-isodynamic magnetic fields, which are generally non-quasisymmetric and which can approximate fields of experimental interest, neoclassical calculations can be carried out analytically more completely than in…
Nuclear fusion using magnetic confinement holds promise as a viable method for sustainable energy. However, most fusion devices have been experimental and as we move towards energy reactors, we are entering into a new paradigm of…
We extend the foil winding homogenization method to magnetic field conforming formulations. We first propose a full magnetic field foil winding formulation by analogy with magnetic flux density conforming formulations. We then introduce the…
An optimized stellarator at finite plasma beta is realized by single-stage optimization of simply modifying the coil currents of the Compact Stellarator with Simple Coils (CSSC)[Yu et al., J. Plasma Physics 88,905880306 (2022)]. The CSSC is…
Bilevel optimization is an important class of optimization problems where one optimization problem is nested within another. While various methods have emerged to address unconstrained general bilevel optimization problems, there has been a…
Knowledge of the structure of the coronal magnetic field is important for our understanding of many solar activity phenomena, e.g. flares and CMEs. However, the direct measurement of coronal magnetic fields is not possible with present…
In this paper, we present new quasi-interpolating spline schemes defined on 3D bounded domains, based on trivariate $C^2$ quartic box splines on type-6 tetrahedral partitions and with approximation order four. Such methods can be used for…
We present a non-conforming least squares method for approximating solutions of second order elliptic problems with discontinuous coefficients. The method is based on a general Saddle Point Least Squares (SPLS) method introduced in previous…
This paper proposes an $O(N)$ fast direct solver for two-dimensional elastic wave scattering problems. The proxy surface method is extended to elastodynamics to obtain shared coefficients for low-rank approximations from discretized…
We propose a new approach for controlling the characteristics of certain mesh faces during optimization of high-order curved meshes. The practical goals are tangential relaxation along initially aligned curved boundaries and internal…
Exploring the origin and properties of magnetic fields is crucial to the development of many fields such as physics, astronomy and meteorology. We focus on the edge element approximation and theoretical analysis of celestial dynamo system…
This work develops optimal preconditioners for the discrete H(curl) and H(div) problems on two-dimensional surfaces by nodal auxiliary space preconditioning [R. Hiptmair, J. Xu: SIAM J. Numer. Anal. \textbf{45}, 2483-2509 (2007)]. In…
We develop and analyze stochastic approximation algorithms for solving nested compositional bi-level optimization problems. These problems involve a nested composition of $T$ potentially non-convex smooth functions in the upper-level, and a…
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…
In Directed Multiway Cut(Dir-MC) the input is an edge-weighted directed graph $G=(V,E)$ and a set of $k$ terminal nodes $\{s_1,s_2,\ldots,s_k\} \subseteq V$; the goal is to find a min-weight subset of edges whose removal ensures that there…
Magnetic shields that use both active and passive components to enable the generation of a tailored low-field environment are required for many applications in science, engineering, and medical imaging. Until now, accurate field nulling, or…
We solve a design optimization problem for deterministic lateral displacement (DLD) device to sort same-size biological cells by their deformability, in particular to sort red blood cells (RBCs) by their viscosity contrast between the fluid…
We investigate the electromagnetic fields in the vacuum exterior of a rotating relativistic star endowed with a magnetic dipole moment, and with the stellar surface behaving as a perfect conductor. While the stellar rotation is treated in…