On solving complex-symmetric eigenvalue problems arising in the design of axisymmetric VCSEL devices

Arbenz, Peter; Chinellato, Oscar

doi:10.1016/j.apnum.2007.01.019

Cited by 6 publications

(4 citation statements)

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“…In the case of the OPAL integration, the main function is playing the role of the "forward solver". To underline the general nature of our approach, in a similar project, the described methods are used for cavity shape optimisation based on [25]. As for the Optimizer component there exists a base class, labeled Simulation as common basis for all Simulation implementations.…”

Section: Implementing a Forward Solvermentioning

confidence: 99%

Parallel general purpose multiobjective optimization framework with application to electron beam dynamics

Neveu

Spentzouris

Adelmann

et al. 2019

Phys. Rev. Accel. Beams

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Particle accelerators are invaluable tools for research in the basic and applied sciences, such as materials science, chemistry, the biosciences, particle physics, nuclear physics and medicine. The design, commissioning, and operation of accelerator facilities is a non-trivial task, due to the large number of control parameters and the complex interplay of several conflicting design goals. The Argonne Wakefield Accelerator facility has some unique challenges resulting from its purpose to carry out advanced accelerator R&D. Individual experiments often have challenging beam requirements, and the physical configuration of the beamlines is often changed to accommodate the variety of supported experiments. The need for rapid deployment of different operational settings further complicates the optimization work that must be done for multiple constraints and challenging operational regimes. One example of this is an independently staged two-beam acceleration experiment which requires the construction of an additional beamline (this is now in progress). The high charge drive beam, well into the space charge regime, must be threaded through small aperture (17.6 mm) decelerating structures. In addition, the bunch length must be sufficiently short to maximize power generation in the decelerator. We propose to tackle this problem by means of multi-objective optimization algorithms which also facilitate a parallel deployment. In order to compute solutions in a meaningful time frame, a fast and scalable software framework is required. In this paper, we present a general-purpose framework for simulation-based multi-objective optimization methods that allows the automatic investigation of optimal sets of machine parameters. Using evolutionary algorithms as the optimizer and OPAL as the forward solver, validation experiments and results of multi-objective optimization problems in the domain of beam dynamics are presented. Optimized solutions for the new high charge drive beamline found by the framework were used to finish the design of a two beam acceleration experiment. The selected solution along with the associated beam parameters is presented.

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Section: Implementing a Forward Solvermentioning

confidence: 99%

Parallel general purpose multiobjective optimization framework with application to electron beam dynamics

Neveu

Spentzouris

Adelmann

et al. 2019

Phys. Rev. Accel. Beams

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“…Eq. ( 2)] time-harmonic Maxwell's equations with perfectly electrically conducting (PEC) boundary conditions (BC) are solved in the evacuated axisymmetric RF cavity parameterized by d. The mixed finite element method (FEM) leads to a generalized eigenvalue problem (GEVP) for each azimuthal mode number m ∈ N 0 [29,30]. For monopole and dipole modes, m = 0 and m = 1, respectively.…”

Section: Constrained Multi-objective Optimization Algorithmmentioning

confidence: 99%

Constrained multiobjective shape optimization of superconducting rf cavities considering robustness against geometric perturbations

Kranjčević

Zadeh

Adelmann

et al. 2019

Phys. Rev. Accel. Beams

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“…In the realm of applied mathematics, complex symmetric matrices appear in the study of quantum reaction dynamics [12,21], electric power modeling [78], the numerical simulation of high-voltage insulators [126], magnetized multicomponent transport [66], thermoelastic wave propagation [136], the maximum clique problem in graph theory [23], elliptically polarized plane waves in continuous media [20], inverse spectral problems for semisimple damped vibrating systems [101], low-dimensional symplectic gravity models [90], the study of decay phenomena [125], scattering matrices in atomic collision theory [22], and the numerical solution of the time-harmonic Maxwell equation in axisymmetric cavity surface emitting lasers [6]. Throughout the years, complex symmetric matrices have also been the focus of sporadic numerical work [7,11,40,43,63,75,84,85,92,105,142,143,152].…”

Section: Introductionmentioning

confidence: 99%

Mathematical and physical aspects of complex symmetric operators

Garcia¹,

Prodan²,

Putinar³

2014

J. Phys. A: Math. Theor.

138

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ABSTRACT. Recent advances in the theory of complex symmetric operators are presented and related to current studies in non-hermitian quantum mechanics. The main themes of the survey are: the structure of complex symmetric operators, C-selfadjoint extensions of C-symmetric unbounded operators, resolvent estimates, reality of spectrum, bases of C-orthonormal vectors, and conjugatelinear symmetric operators. The main results are complemented by a variety of natural examples arising in field theory, quantum physics, and complex variables.

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On solving complex-symmetric eigenvalue problems arising in the design of axisymmetric VCSEL devices

Cited by 6 publications

References 50 publications

Parallel general purpose multiobjective optimization framework with application to electron beam dynamics

Parallel general purpose multiobjective optimization framework with application to electron beam dynamics

Constrained multiobjective shape optimization of superconducting rf cavities considering robustness against geometric perturbations

Mathematical and physical aspects of complex symmetric operators

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