Experiments on a Parallel Nonlinear Jacobi–Davidson Algorithm

AbstractThe Jacobi–Davidson (JD) algorithm is very well suited for the computation of a few eigen-pairs of large sparse complex symmetric nonlinear eigenvalue problems. The performance of JD crucially depends on the treatment of the so-called correction equation, in particular the preconditioner, and the initial vector. Depending on the choice of the spectral shift and the accuracy of the solution, the convergence of JD can vary from linear to cubic. We investigate parallel preconditioners for the Krylov space method used to solve the correction equation.We apply our nonlinear Jacobi–Davidson (NLJD) method to quadratic eigenvalue problems that originate from the time-harmonic Maxwell equation for the modeling and simulation of resonating electromagnetic structures

Investigation of the Purcell effect in photonic crystal cavities with a 3D Finite Element Maxwell Solver

Photonic crystal cavities facilitate novel applications demanding the efficient emission of incoherent light. This unique property arises when combining a relatively high quality factor of the cavity modes with a tight spatial constriction of the modes. While spontaneous emission is desired in these applications the stimulated emission must be kept low. A measure for the spontaneous emission enhancement is the local density of optical states (LDOS). Due to the complicated three dimensional geometry of photonic crystal cavities the LDOS quantity has to be computed numerically. In this work, we present the computation of the LDOS by means of a 3D Finite Element (FE) Maxwell Solver. The solver applies a sophisticated symmetry handling to reduce the problem size and provides perfectly matched layers to simulate open boundaries. Different photonic crystal cavity designs have been investigated for their spontaneous emission enhancement by means of this FE solver. The simulation results have been compared to photoluminescence characterizations of fabricated cavities. The excellent agreement of simulations and characterizations results confirms the performance and the accuracy of the 3D FE Maxwell Solve

Investigation of the Purcell effect in photonic crystal cavities with a 3D Finite Element Maxwell Solver

Photonic crystal cavities facilitate novel applications demanding the efficient emission of incoherent light. This unique property arises when combining a relatively high quality factor of the cavity modes with a tight spatial constriction of the modes. While spontaneous emission is desired in these applications the stimulated emission must be kept low. A measure for the spontaneous emission enhancement is the local density of optical states (LDOS). Due to the complicated three dimensional geometry of photonic crystal cavities the LDOS quantity has to be computed numerically. In this work, we present the computation of the LDOS by means of a 3D Finite Element (FE) Maxwell Solver. The solver applies a sophisticated symmetry handling to reduce the problem size and provides perfectly matched layers to simulate open boundaries. Different photonic crystal cavity designs have been investigated for their spontaneous emission enhancement by means of this FE solver. The simulation results have been compared to photoluminescence characterizations of fabricated cavities. The excellent agreement of simulations and characterizations results confirms the performance and the accuracy of the 3D FE Maxwell Solve

A fast and scalable low dimensional solver for charged particle dynamics in large particle accelerators

Particle accelerators are invaluable tools for research in the basic and applied sciences, in fields 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. We propose to tackle this problem by means of multi-objective optimization algorithms which also facilitate massively parallel deployment. In order to compute solutions in a meaningful time frame, that can even admit online optimization, we require a fast and scalable software framework. In this paper, we focus on the key and most heavily used component of the optimization framework, the forward solver. We demonstrate that our parallel methods achieve a strong and weak scalability improvement of at least two orders of magnitude in today's actual particle beam configurations, reducing total time to solution by a substantial factor. Our target platform is the Blue Gene/P (Blue Gene/P is a trademark of the International Business Machines Corporation in the United States, other countries, or both) supercomputer. The space-charge model used in the forward solver relies significantly on collective communication. Thus, the dedicated TREE network of the platform serves as an ideal vehicle for our purposes. We demonstrate excellent strong and weak scalability of our software which allows us to perform thousands of forward solves in a matter of minutes, thus already allowing close to online optimization capabilit

REALISTIC 3-DIMENSIONAL EIGENMODAL ANALYSIS OF ELECTROMAGNETIC CAVITIES USING SURFACE IMPEDANCE BOUNDARY CONDITIONS

Abstract The new X-ray Free Electron Laser (SwissFEL) at the Paul Scherrer Institute (PSI) employs, among many other radio frequency elements, a transverse deflecting cavity for beam diagnostics. Since the fabrication process is expensive, an accurate 3-D eigenmodal analysis is indispensable. The software package Femaxx has been developed for solving large scale eigenvalue problems on distributed memory parallel computers. Usually, it is sufficient to assume that the tangential electric field vanishes on the cavity wall (PEC boundary conditions). Of course, in reality, the cavity wall is conductive such that the tangential electrical field on the wall is nonzero. In order to more realistically model the electric field we impose surface impedance boundary conditions (SIBC) arising from the skin effect model. The resulting nonlinear eigenvalue problem is solved with a nonlinear Jacobi-Davidson method. We demonstrate the performance of the method. First, we investigate the fundamental mode of a pillbox cavity. We study resonance, skin depth and quality factor as a function of the cavity wall conductivity. Second, we analyze the transverse deflecting cavity of the SwissFEL to assess the capability of the method for technologically relevant problems. FORMULATION OF THE PROBLEM We wish to calculate the resonant frequencies and the corresponding field distribution in a dielectric electromagnetic cavity. The cavity wall Γ is assumed to be of arbitrary shape; there is no aperture or hole in Γ. The surface conductivity σ s of Γ is large but finite. The interior Ω of the cavity is assumed to be source-free, and is characterized by (µ 0 µ r , ε 0 ε r ). µ 0 and ε 0 are the magnetic permeability and electric permittivity in free space. µ r and ε r are relative magnetic permeability and relative electric permittivity, respectively. At microwave frequencies, µ r and ε r can be assumed to be non-dispersive. In the time-harmonic regime, after eliminating the electric field E(x), the magnetic field H(x) satisfies Here, k 0 =ω √ µ 0 ε 0 is the complex wave number in free space,ω = ω + iα is the complex angular frequency with ω the angular frequency and α the exponential decay rate. * hguo@inf. ethz.ch † arbenz@inf. ethz.ch ‡ benedikt.oswald@ps i.ch We use the surface impedance boundary condition (SIBC) Here, Z s is the complex surface impedance and n the surface normal vector pointing outwards. We employ Z s based on the theoretical skin effect model [2] where σ s is the surface conductivity, and δ is the skin depth. The real part of Z s is the surface resistivity, i.e., The skin depth δ is [2] δ depends on the angular frequency ω. Note that the skin effect model is appropriate only if σ s is large enough such that (according to The finite element method (FEM) is a suitable method for arbitrary geometrical scales. In order to apply the FEM we use the weak form of Eq (1), see Ω µ r H · ∇q dx = 0. Here, V denotes the functions in H(curl; Ω) that satisfy the SIBC boundary conditions and W =

Mechanical competence of bone-implant systems can accurately be determined by image-based micro-finite element analyses

The precise failure mechanisms of bone implants are still incompletely understood. Micro-computed tomography in combination with finite element analysis appears to be a potent methodology to determine the mechanical stability of bone-implant constructs. To assess this microstructural finite element (μFE) analysis approach, pull-out tests were designed and conducted on ten sheep vertebral bodies into which orthopedic screws were inserted.μFE models of the same bone-implant constructs were then built and solved, using a large-scale linear FE-solver.μFE calculated pull-out strength correlated highly with the experimentally measured pull-out strength (r 2= 0.87) thereby statistically supporting theμFE approach. These results suggest that bone-implant constructs can be analyzed usingμFE in a detailed and unprecedented way. This could potentially facilitate the development of future implant designs leading to novel and improved fracture fixation method