# Roman Geus's research while affiliated with Paul Scherrer Institut and other places

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## Publications (21)

Synchrotron X-ray tomographic microscopy is a powerful technique which allows fast non-destructive, high resolution, quantitative volumetric investigations on diverse samples. Highly brilliant X-rays delivered by third generation synchrotron facilities coupled with modern detector technology permit routinely acquisition of high resolution tomograms...

We present experiments with two new solvers for large sparse symmetric matrix eigenvalue problems: (1) the implicitly restarted
Lanczos algorithm and (2) the Jacobi-Davidson algorithm. The eigenvalue problems originate from in the computation of a few
of the lowest frequencies of standing electromagnetic waves in cavities that have been discretized...

We report on a parallel implementation of the Jacobi–Davidson algorithm to compute a few eigenvalues and corresponding eigenvectors of a large real symmetric generalized matrix eigenvalue problemThe eigenvalue problem stems from the design of cavities of particle accelerators. It is obtained by the finite element discretization of the time-harmonic...

We investigate eigensolvers for computing a few of the smallest eigenvalues of a generalized eigenvalue problem resulting from the finite element discretization of the time independent Maxwell equation. Various multilevel preconditioners are employed to improve the convergence and memory consumption of the Jacobi–Davidson algorithm and of the local...

Software used in scientific computing is traditionally developed using compiled languages for the sake of maximal performance. However, for most applications, the time-critical portion of the code that requires the efficiency of a compiled language, is confined to a small set of well-defined functions. Implementing the remaining part of the applica...

We report on a parallel implementation of the Jacobi–Davidson algorithm to compute a few eigenvalues and corresponding eigenvectors of a large real symmetric generalized matrix eigenvalue problem. The eigenvalue problem stems from the design of cavities of particle accelerators. It is obtained by the finite element discretization of the time-harmon...

Start to end simulations are discussed in the light of our plans for a 3 mA, 1.8MWproton beam at the PSI cyclotron facility [1].

We report on a parallel implementation of the Jacobi–Davidson (JD) to compute a few eigenpairs of a large real symmetric generalized matrix eigenvalue problem
$$A \mathbf{x} = \lambda M \mathbf{x}, \qquad C^T \mathbf{x} = \mathbf{0}. $$ The eigenvalue problem stems from the design of cavities of particle accelerators. It is obtained by the finite e...

This paper describes our experience with the redesign and reimplementation of a large-scale application from accelerator physics using this mixed1 language programming approach with Python and C

The advanced Maxwell eigenvalue solver PyFemax is evolving from a research project into a mature simulation tool for RF-cavity design. Its object oriented design, based on the scripting language Python, gives flexibility and portability. For high performance, the time-critical parts are written in C. Presently, PyFemax relies on the Jacobi-Davidson...

The sparse matrix–vector product is an important computational kernel that runs ineffectively on many computers with super-scalar RISC processors. In this paper we analyse the performance of the sparse matrix–vector product with symmetric matrices originating from the FEM and describe techniques that lead to a fast implementation. It is shown how t...

this paper we report on our continuing investigations on eigensolvers and their preconditioning. In contrast to [7] we conduct our experiments on a domain that approximates the new cavity design for the 590 MeV ring cyclotron at the Paul Scherrer Institute (PSI) in Villigen, Switzerland, see Fig. 1 on the right-hand side. The outline of the paper i...

The sparse matrix-vector product is an important computational kernel that runs ineffectively on many computers with super-scalar RISC processors. In this paper we analyse the performance of the sparse matrix-vector product with symmetric matrices originating from the FEM and describe techniques that lead to a fast implementation. It is shown how t...

We present experiments with various solvers for large sparse generalized symmetric matrix eigenvalue problems. These problems occur in the computation of a few of the lowest frequencies of standing electromagnetic waves in resonant cavities with the finite element method. The solvers investigated are (1) subspace iteration, (2) block Lanczos algori...

. We report on a comparison of the implicitly restarted Lanczos algorithm as implemented in ARPACK and the Jacobi-Davidson algorithm for solving large sparse generalized symmetric matrix eigenvalue problems. These problems occur in the computation of a few of the lowest frequencies of standing electromagnetic waves in cavity resonators. The computa...

. We present experiments with two new solvers for large sparse symmetric matrix eigenvalue problems: (1) the implicitly restarted Lanczos algorithm and (2) the Jacobi-Davidson algorithm. The eigenvalue problems originate from in the computation of a few of the lowest frequencies of standing electromagnetic waves in cavities that have been discretiz...

We investigate eigensolvers for computing a few of the smallest eigenvalues of a generalized eigenvalue problem resulting from the finite element discretization of the time independent Maxwell equation. Various multilevel preconditioners are employed to improve the convergence and memory consumption of the Jacobi-Davidson algorithm and of the local...

elec finite elements to discretise Maxwell's equations. Several algorithms dealing with spurious modes are incor- porated. The Jacobi-Davidson algorithm (JDSYM) is used for computing selected eigenpairs of the resulting large sparse symmetric eigenvalue problem. PyFemax offers some visualisation and postprocessing features. PyFemax is implemented u...

A summary of activities that envisage a source to tar-get simulation of the PSI cyclotron complex is presented. Our aim is to gain a quantitative understanding of com-plex phenomena in our machines and beam lines, includ-ing three-dimensional space charge effects, beam cavity in-teraction, collimation, beam neutralisation and extraction mechanism....

The numerical computation of eigenfrequencies and eigenmodal fields of large accelerator cavities, based on full-wave, three-dimensional models, has attracted consid- erable interest in the recent past. In particular, it is of vital interest to know the performance characteristics, such as resonance frequency, quality figures and the modal fields,...

## Citations

... This project is a collaborative effort of PSI and the Institute of Computational Science at ETH Zurich. femaXX is the parallelised successor of pyfemax and femax++ [4]. It is intended to run very large scale eigenmode, quality factor and gap voltage computations for complicated RF structures like the one in the COMET cyclotron. ...

Reference: PARALLEL EIGENMODE COMPUTATIONS USING FEMAXX

... Omega3P and PyFemax have been used [75, 27] for a cross-check of the eigenmode calculation of the COMET cyclotron rf-structure to be delivered by ACCEL GmbH for the PSI PROSCAN project for proton-therapy (seeFig. 3.1). ...

... The above formula (6) is also introduced in [13] and [14]. It is easy to know dim( ...

... To find the interior eigenvalues, several eigenvalue solvers have been proposed. The solvers range from the Jacobi-Davidson methods [3][4][5][6][7][8][9][10][11] to the shift-and-invert type methods, including the inverse power methods [4,12,2,13] and Lanczos/Arnoldi methods [4,6,14]. As the GEVP are large, iterative methods are used to solve the resulting linear systems within the eigenvalue solvers. ...

... The stability of the microscope and the precision of the sample stages allow one to feed the angular projections directly into the standard tomographic reconstruction algorithms . The Fourier based tomographic reconstruction routine (Marone et al., 2008) used for parallel beam tomography at the TOMCAT beamline was applied to all data. The resulting volumes capture the spatial distribution of structures based on their phase retardation action on the probing X-rays. ...

... Codes for simulating space charge dominated beams taking into account the effect of neighbouring turns are ready. Validated results to provide insight into the new situation will soon be available [9]. ...

... In order to avoid spurious modes we approximate the electric field e by Nédélec (or edge) ele- ments [20]. The Lagrange multiplier (a function) introduced to treat properly the divergence free condition is approximated by Lagrange (or nodal) finite elements [3]. In this paper we consider a parallel eigensolver for computing a few of the smallest eigenvalues and corresponding eigenvectors of (1.2) as efficiently as possible with regard to execution time and memory cost. ...

... This is in contrast to VFEM, where the normal discontinuity of edge elements leads to the formation of artificial charges at element interfaces, thus increasing the total divergence of the solutions; this problem worsens with mesh refinement. 50 Note that in VFEM, the zero-frequency spurious solutions are separated by filtering out the null-space of the curl operator from the spectrum using iterative techniques, 51,52 or by finding eigenvalues in the interior of the spectrum. This is necessary, since if the physical solution space is not normal to the null space, the physical solutions will be polluted by null vectors. ...

... Therefore, we apply Forward-Euler method to obtain a numerical co-simulation of the equivalent switched system. By setting an integration step-size Dt=0.0001 and initial conditions (x 1 =0.1,x 2 =0,x 3 =0,x 4 =0.1,x 5 =0,x 6 =0,x 7 =0.1,x 8 =0,x 9 =0), the resulting chaotic attractor by plotting state variables ðx 1 ;x 4 ;x 7 Þ, which correspond to the original state variables ðx 1 ; x 2 ; x 3 Þ, is shown in Fig. 2. Due to Python is a multi-paradigm high-level programming language focused on generating high-performance algorithms [42,43], we choose it for developing the necessary script to get the embedded implementation of (13) in an ARM SoC board. Accordingly, the aforementioned Python Pseudocode is given in the Appendix A. Using the low-cost comercial ARM SoC Broadcom BCM22835 [44,45], (13) is physical implemented. ...

... For a point d, a mesh of half of the cross section of the corresponding cavity is created using the Gmsh [44] C þþ API. In the FEM linear elements are used, and the resulting GEVPs are solved using the symmetric Jacobi-Davidson algorithm [45]. ...