Uncertainty Quantification for Complex RF-structures Using the State-space Concatenation Approach

In various applications of computational engineering and accelerator physics, the computation of the electromagnetic behavior of a structure is of crucial importance for the design and operation. The electromagnetic properties of the structure depend on its geometry, which, for real-life radio-frequency (RF) structures, generally deviates from their design values due to fabrication tolerances and operation. To make assessments about the effects of such deviations as well as to employ robust optimizations, a so-called uncertainty quantification (UQ) is applied. For large and complex structures such computations are heavily demanding and cannot be carried out using standard brute-force approaches. In this paper, we propose a combination of established techniques to perform UQ for long and complex structures, where the uncertainty is located only in parts of the structure. As exemplary structure, we investigate the third-harmonic cavity, which is being used at the FLASH accelerator at DESY, assuming an uncertain geometry of the left higher order mode coupler. The investigation is carried out using the so-called polynomial chaos expansion (gPC). For that, the repeated numerical solution of Maxwell’s equations is necessary. Usually, such investigations are carried out on supercomputers or small computer clusters with heavily parallelized code. Due to the fact that maximum-performance computational infrastructure is scarce and expensive, the electromagnetic properties are being computed on standard workstation computers using a newly proposed non-overlapping domain decomposition scheme named State-Space Concatenation (SSC) which is based on model-order reduction of the decomposed segments. Using the SSC scheme has the most important advantage that only the uncertain part of the structure, in our case the left coupler, needs to be recomputed when using a non-intrusive scheme like gPC. In comparison to the huge computational demand of a straightforward simulation, the combination of uncertainty quantification and model-order reduction allows for a reasonable improvement of the computational efficiency. Both schemes can be separately applied to structures related to accelerator physics. Yet, just their combination will enable the investigation of long and complex structures beyond the scope of standard approaches.