Jukka I. Toivanen

Electromagnetic Sensitivity Analysis and Shape Optimization Using Method of Moments and Automatic Differentiation

Sensitivity analysis is an important part of gradient-based optimization of electromagnetic devices. We demonstrate how sensitivity analysis can be incorporated into an existing in-house method of moments solver with a relatively small amount of labor by using a technique called automatic differentiation (AD). This approach enables us to obtain (geometrical) sensitivities of the discrete solution with accuracy up to numerical precision. We compare the assembly time and memory usage of the modified and original solvers. Moreover, we optimize the shape of a dipole antenna and the dimensions of a Yagi-Uda array using the presented AD technique, traditional response level finite difference sensitivities, and so-called feasible adjoint sensitivity technique.

Shape Sensitivity Analysis and Gradient-Based Optimization of Large Structures Using MLFMA

A fast method for computing the action of shape-differentiated electric field integral equation (EFIE) system matrix to a vector is derived exploiting the multilevel fast multipole algorithm (MLFMA). The proposed method is used in conjunction with the adjoint-variable method (AVM) to compute the shape gradient of arbitrary objective functions depending on shape of a metallic scatterer. The method is demonstrated numerically by optimizing the shape of a parabolic reflector illuminated with a half-wave dipole.

COMPARISON OF CPML IMPLEMENTATIONS FOR THE GPU-ACCELERATED FDTD SOLVER

Three distinctively difierent implementations of convolu- tional perfectly matched layer for the FDTD method on CUDA enabled graphics processing units are presented. All implementations store ad- ditional variables only inside the convolutional perfectly matched lay- ers, and the computational speeds scale according to the thickness of these layers. The merits of the difierent approaches are discussed, and a comparison of computational performance is made using complex real-life benchmarks.

Topology optimization in Bernoulli free boundary problems

In this work we consider the topology optimization of systems governed by the external Bernoulli free boundary problem arising, for example, from the mathematical modelling of electro-chemical machining. In this work we combine, for the first time, the so-called pseudo-solid approach to the solution of governing free boundary problems and the level set method, which is used to define the design domain. Previous studies of the problem showed a tendency towards topological changes in the design, which can now automatically take place thanks to level set parametrization. The scalar function used in the level set method is parametrized using radial basis functions, converting the problem into a parametric optimization problem, which is solved using a gradient-based method.

Simulation software for flow of fluid with suspended point particles in complex domains: application to matrix diffusion

Matrix diffusion is a phenomenon in which tracer particles convected along a flow channel can diffuse into porous walls of the channel, and it causes a delay and broadening of the breakthrough curve of a tracer pulse. Analytical and numerical methods exist for modeling matrix diffusion, but there are still some features of this phenomenon, which are difficult to address using traditional approaches. To this end we propose to use the lattice-Boltzmann method with point-like tracer particles. These particles move in a continuous space, are advected by the flow, and there is a stochastic force causing them to diffuse. This approach can be extended to include particle-particle and particle-wall interactions of the tracer. Numerical results that can also be considered as validation of the LBM approach, are reported. As the reference we use recently-derived analytical solutions for the breakthrough curve of the tracer.

Implementation of sparse forward mode automatic differentiation with application to electromagnetic shape optimization

In this paper, we present the details of a simple lightweight implementation of the so-called sparse forward mode automatic differentiation (AD) in the C++programming language. Our implementation and the well-known ADOL-C tool (which utilizes taping and compression techniques) are used to compute Jacobian matrices of two nonlinear systems of equations from the MINPACK-2 test problem collection. Timings of the computations are presented and discussed. Moreover, we perform the shape sensitivity analysis of a time-harmonic Maxwell equation solver using our implementation and the tapeless mode of ADOL-C, which implements the dense forward mode AD. It is shown that the use of the sparse forward mode can save computation time even though the total number of independent variables in this example is quite small. Finally, numerical solution of an electromagnetic shape optimization problem is presented.

Coupling of lattice-Boltzmann solvers with suspended particles using the MPI intercommunication framework

Abstract The MPI intercommunication framework was used for coupling of two lattice-Boltzmann solvers with suspended particles, which model advection and diffusion respectively of these particles in a carrier fluid. Simulation domain was divided into two parts, one with advection and diffusion, and the other with diffusion only (no macroscopic flow). Particles were exchanged between these domains at their common boundary by a direct process to process communication. By analysing weak and strong scaling, it was shown that the linear scaling characteristics of the lattice-Boltzmann solvers were not compromised by their coupling.

An Automatic Differentiation Based Approach to the Level Set Method

This paper discusses an implementation of the parametric level set method. Adjoint approach is used to perform the sensitivity analysis, but contrary to standard implementations, the state problem is differentiated in its discretized form. The required partial derivatives are computed using tools of automatic differentiation, which avoids the need to derive the adjoint problem from the governing partial differential equation. The augmented Lagrangian approach is used to enforce volume constraints, and a gradient based optimization method is used to solve the subproblems. Applicability of the method is demonstrated by repeating well known compliance minimization studies of a cantilever beam and a Michell type structure. The obtained topologies are in good agreement with reference results.

LBM simulations of matrix diffusion with sorption

Matrix diffusion is a phenomenon in which tracer particles convected along a flow channel can diffuse into porous walls of the channel, and it causes a delay and broadening of the breakthrough curve of the tracer pulse. The lattice-Boltzmann method is a popular tool for simulating flow through porous materials, and for similar reasons it is an attractive tool for modeling the matrix diffusion phenomenon. In this work sorption of the tracer particles is also included in such simulations with this method. The proposed approach is compared with conventional methods for modeling matrix diffusion phenomena.