0000000000006890
AUTHOR
Jukka I. Toivanen
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.
A new method for creating sparse design velocity fields
We present a novel method for the computation of mesh node sensitivities with respect to the boundary node movement. The sensitivity field is sparse in a sense that movement of each boundary node affects only given amount of inner mesh nodes, which can result in considerable savings in the storage space. The method needs minimal control from the user, and it does not place any restrictions (such as block structure) on the mesh. Use of the method is demonstrated with a shape optimization problem using CAD-free parametrization. A solution to the classical die-swell free boundary problem by coupling the boundary node locations with the state variables is also presented. In that case, sparsity …
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…
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.
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 …
An elementary formula for computing shape derivatives of EFIE system matrix
We derive analytical shape derivative formulas of the system matrix representing electric field integral equation discretized with Raviart-Thomas basis functions. The arising integrals are easy to compute with similar methods as the entries of the original system matrix. The results are compared to derivatives computed with automatic differentiation technique and finite differences, and are found to be in excellent agreement.
On shape differentiation of discretized electric field integral equation
Abstract This work presents shape derivatives of the system matrix representing electric field integral equation discretized with Raviart–Thomas basis functions. The arising integrals are easy to compute with similar methods as the entries of the original system matrix. The results are compared to derivatives computed with automatic differentiation technique and finite differences, and are found to be in an excellent agreement. Furthermore, the derived formulas are employed to analyze shape sensitivity of the input impedance of a planar inverted F-antenna, and the results are compared to those obtained using a finite difference approximation.
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.
Gradient-based shape optimisation of ultra-wideband antennas parameterised using splines
Methodology enabling the gradient-based optimisation of antennas parameterised using B-splines is presented. Use of the spline parametrisation allows us to obtain versatile new shapes, whereas the geometry can be represented with a small set of design variables. Moreover, good control over admissible geometries is retained. Advantages of gradient-based optimisation methods are quick convergence, and the fact that the obtained design can be guaranteed to be a local optimum. Focus of this study is to present techniques that enable the computation of exact gradients of the discrete problem, even though the complexity of the geometries does not permit establishing analytical expressions for the…
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 sens…