The Unified-FFT Method for Fast Solution of Integral Equations as Applied to Shielded-Domain Electromagnetics

Electromagnetic (EM) solvers are widely used within computer-aided design (CAD) to improve and ensure success of circuit designs. Unfortunately, due to the complexity of Maxwell\u27s equations, they are often computationally expensive. While considerable progress has been made in the realm of speed-enhanced EM solvers, these fast solvers generally achieve their results through methods that introduce additional error components by way of geometric approximations, sparse-matrix approximations, multilevel decomposition of interactions, and more. This work introduces the new method, Unified-FFT (UFFT). A derivative of method of moments, UFFT scales as O(N log N), and achieves fast analysis by the unique combination of FFT-enhanced matrix fill operations (MFO) with FFT-enhanced matrix solve operations (MSO). In this work, two versions of UFFT are developed, UFFT-Precorrected (UFFT-P) and UFFT-Grid Totalizing (UFFT-GT). UFFT-P uses precorrected FFT for MSO and allows the use of basis functions that do not conform to a regular grid. UFFT-GT uses conjugate gradient FFT for MSO and features the capability of reducing the error of the solution down to machine precision. The main contribution of UFFT-P is a fast solver, which utilizes FFT for both MFO and MSO. It is demonstrated in this work to not only provide simulation results for large problems considerably faster than state of the art commercial tools, but also to be capable of simulating geometries which are too complex for conventional simulation. In UFFT-P these benefits come at the expense of a minor penalty to accuracy. UFFT-GT contains further contributions as it demonstrates that such a fast solver can be accurate to numerical precision as compared to a full, direct analysis. It is shown to provide even more algorithmic efficiency and faster performance than UFFT-P. UFFT-GT makes an additional contribution in that it is developed not only for planar geometries, but also for the case of multilayered dielectrics and metallization. This functionality is particularly useful for multi-layered printed circuit boards (PCBs) and integrated circuits (ICs). Finally, UFFT-GT contributes a 3D planar solver, which allows for current to be discretized in the z-direction. This allows for similar fast and accurate simulation with the inclusion of some 3D features, such as vias connecting metallization planes

Salient object subitizing

We study the problem of salient object subitizing, i.e. predicting the existence and the number of salient objects in an image using holistic cues. This task is inspired by the ability of people to quickly and accurately identify the number of items within the subitizing range (1–4). To this end, we present a salient object subitizing image dataset of about 14 K everyday images which are annotated using an online crowdsourcing marketplace. We show that using an end-to-end trained convolutional neural network (CNN) model, we achieve prediction accuracy comparable to human performance in identifying images with zero or one salient object. For images with multiple salient objects, our model also provides significantly better than chance performance without requiring any localization process. Moreover, we propose a method to improve the training of the CNN subitizing model by leveraging synthetic images. In experiments, we demonstrate the accuracy and generalizability of our CNN subitizing model and its applications in salient object detection and image retrieval.This research was supported in part by US NSF Grants 0910908 and 1029430, and gifts from Adobe and NVIDIA. (0910908 - US NSF; 1029430 - US NSF)https://arxiv.org/abs/1607.07525https://arxiv.org/pdf/1607.07525.pdfAccepted manuscrip

Portable parallel stochastic optimization for the design of aeropropulsion components

This report presents the results of Phase 1 research to develop a methodology for performing large-scale Multi-disciplinary Stochastic Optimization (MSO) for the design of aerospace systems ranging from aeropropulsion components to complete aircraft configurations. The current research recognizes that such design optimization problems are computationally expensive, and require the use of either massively parallel or multiple-processor computers. The methodology also recognizes that many operational and performance parameters are uncertain, and that uncertainty must be considered explicitly to achieve optimum performance and cost. The objective of this Phase 1 research was to initialize the development of an MSO methodology that is portable to a wide variety of hardware platforms, while achieving efficient, large-scale parallelism when multiple processors are available. The first effort in the project was a literature review of available computer hardware, as well as review of portable, parallel programming environments. The first effort was to implement the MSO methodology for a problem using the portable parallel programming language, Parallel Virtual Machine (PVM). The third and final effort was to demonstrate the example on a variety of computers, including a distributed-memory multiprocessor, a distributed-memory network of workstations, and a single-processor workstation. Results indicate the MSO methodology can be well-applied towards large-scale aerospace design problems. Nearly perfect linear speedup was demonstrated for computation of optimization sensitivity coefficients on both a 128-node distributed-memory multiprocessor (the Intel iPSC/860) and a network of workstations (speedups of almost 19 times achieved for 20 workstations). Very high parallel efficiencies (75 percent for 31 processors and 60 percent for 50 processors) were also achieved for computation of aerodynamic influence coefficients on the Intel. Finally, the multi-level parallelization strategy that will be needed for large-scale MSO problems was demonstrated to be highly efficient. The same parallel code instructions were used on both platforms, demonstrating portability. There are many applications for which MSO can be applied, including NASA's High-Speed-Civil Transport, and advanced propulsion systems. The use of MSO will reduce design and development time and testing costs dramatically

Development of iterative techniques for the solution of unsteady compressible viscous flows

The development of efficient iterative solution methods for the numerical solution of two- and three-dimensional compressible Navier-Stokes equations is discussed. Iterative time marching methods have several advantages over classical multi-step explicit time marching schemes, and non-iterative implicit time marching schemes. Iterative schemes have better stability characteristics than non-iterative explicit and implicit schemes. In this work, another approach based on the classical conjugate gradient method, known as the Generalized Minimum Residual (GMRES) algorithm is investigated. The GMRES algorithm has been used in the past by a number of researchers for solving steady viscous and inviscid flow problems. Here, we investigate the suitability of this algorithm for solving the system of non-linear equations that arise in unsteady Navier-Stokes solvers at each time step

Computer Aided Verification

This open access two-volume set LNCS 13371 and 13372 constitutes the refereed proceedings of the 34rd International Conference on Computer Aided Verification, CAV 2022, which was held in Haifa, Israel, in August 2022. The 40 full papers presented together with 9 tool papers and 2 case studies were carefully reviewed and selected from 209 submissions. The papers were organized in the following topical sections: Part I: Invited papers; formal methods for probabilistic programs; formal methods for neural networks; software Verification and model checking; hyperproperties and security; formal methods for hardware, cyber-physical, and hybrid systems. Part II: Probabilistic techniques; automata and logic; deductive verification and decision procedures; machine learning; synthesis and concurrency. This is an open access book

The impact of treewidth on ASP grounding and solving of Answer Set Programs

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