Conference Agenda

Projection-based model order reduction enables efficient high-fidelity low-frequency dosimetry simulations based on pre-computed solution vectors of the large system. Since most of these vectors provide proximal information about the system, the information-theoretic framework called maximum entropy snapshot sampling can be used to reduce them to the only essential ones from which a reduced basis can be constructed. Although this framework is memory efficient, it has a computational bottleneck in constructing the required recurrence matrix due to the use of state-recurrence analysis. Therefore, this work aims to improve this framework by using energy-variation analysis.

The proper orthogonal decomposition (POD) is commonly applied for the model order reduction (MOR) of parametric problems. The method generates a reduced basis from the left singular vectors of a matrix consisted by a set of snapshot solutions. The basis represents a lower dimensional subspace where the solutions lie on. Thus, it can be utilized for order reduction of the original problem. The singular value decomposition (SVD) of the snapshot matrix is a key step to obtain the reduced basis. However, a prerequisite of SVD is that the snapshots have the same degrees of freedom, so that they can consist a rectangular matrix. This prerequisite brings difficulty for the MOR based on POD for parametric problems involving varying geometric parameters. In this work, we propose to use an interface adaptive background mesh to assure the consistence of snapshot solution vector lengths with varying geometry. The method is applied in a preliminary numerical example that solves a parametric electrostatic problem with varying geometry.

The magnetically implicit single-field finite-difference time-domain (MI-SF-FDTD) scheme was recently proposed as a promising direction of algorithm development to relax the stability condition of the explicit leapfrog FDTD scheme. However, its applicability is still limited to two-dimensional problems. In this work, the MI-SF-FDTD is extended to three-dimensional (3-D) open-region problems. For this purpose, the surface impedance absorbing boundary condition is incorporated in the 3-D MI-SF-FDTD scheme. Its numerical stability, computational efficiency and absorption performance are assessed in applications to closed and open problems.

We introduce a new transmission condition for the domain decomposition method with application in particle accelerator problems. The new transmission condition combines a modal decomposition approach for guided-wave propagation with the commonly used technique based on the free-space radiation condition. This significantly improves the convergence properties of the domain decomposition method in guided wave structures, while avoiding the need to repeatedly solve costly auxiliary problems. As an important application, we consider the computation of electromagnetic fields in a large accelerator cavity. This example illustrates the accuracy of the method and demonstrates its numerical efficiency in the simulation of electromagnetically large structures.

In this paper, an integral equation method is proposed for the modeling of carbon fiber-reinforced polymers. To keep the number of degrees of freedom low, the fibers are modeled using a thin-wire approximation. The occasional contact points between the fibers are taken into account by lumped element resistors. The latter is incorporated into the discretized linear equation system by introducing zigzag basis functions, that enable the currents inside the fibers to jump at the contact points. This approach enables the analysis of a unit cell consisting of hundreds of fibers, and the impact of the distribution of the contact points on the impedance change of an eddy current probe coil.