The present work deals with simulation methods for rigid bodies and deformable bodies. In the first chapter you can find research of some methods for simulation of rigid body physics with emphasis on method used in open source physics engine Bullet. In second chapter you can find methods for simulation of deformable bodies, again with emphasis on Bullet physics engine. In last chapter model order reduction technique is presented. This method enables to reduce system of ordinary differential equations. These equations come for example from applying finite element method to partial differential equations describing motion of elastic body. The technique is studied on bar truss systems. Powered by TCPDF (www.tcpdf.org)

Modeling and design of high frequency electronic systems such as antennas and microwave devices require the rigorous numerical solution of Maxwell’s equa- tions. The frequency-domain (time-harmonic) tangential vector finite element method (TVFEM) for Maxwell equations results in a second-order dynamical electromagnetic model that must be repeatedly solved for multiple frequencies, excitation or material parameters each design loop. This leads to extremely long design turnaround that often is not optimal. This work will propose an accurate, error controllable and ef- ficient multi-parametric model order reduction scheme that significantly accelerate these parameters sweep. At the core of this work is the proper orthogonal decompo- sition (POD) sampling technique and balanced truncation (BT) algorithm that are used to reduce multi-parameter spaces that include frequency, material parameters and infinite array scan angles. The proposed methodology employs a novel computa- tional scheme based on adaptive POD sampling and the singular value decomposition (SVD) of the low-rank Hankel matrix. Numerical examples confirm the significant time savings and good accuracy of the method for a diverse set of high-frequency electromagnetic systems.

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The thesis presents xavier, a novel tool-set for model checking of concurrent x86-64 assembly programs, via Partial Order Reduction (POR). xavier{} presents a realistic platform for systematically exploring and analyzing the state-space of concurrent x86 assembly programs, with the aim of detecting bugs via assertion failures in mainstream programs. Recently, a number of state-of-the-art model checking solutions have been introduced to efficiently explore the state-space of concurrent programs, using POR algorithms. However, such solutions are inefficient while analyzing stateful programming languages, such as the x86 assembly language, due to their low level of abstraction. To this end, xavier{} makes two contributions: i) a novel order-sensitivity based POR algorithm, that is applicable to concurrent x86 assembly, ii) an x86 machine-model that can accurately perform relaxed-consistency emulation of concurrent x86 assembly, without the need for any translations. We demonstrate the applicability of xavier{} through an evaluation on several classical mutual-exclusion benchmarks and mainstream benchmarks from the Userspace Read-Copy-Update (URCU) concurrency library, where the benchmarks range from $250-3700$ lines of x86 assembly. The framework is the first that supports systematic model checking of concurrent x86 assembly programs, and the effectiveness of xavier{} is demonstrated by reproducing a concurrency issue of threads accessing intermediate states in the URCU library, which stems from an assumption violation. / Master of Science / Sound verification of multi-threaded programs necessitate a systematic analysis of program state-spaces that result from thread interactions. Consequently, model-checking cite{godefroid1997model, Clarke2018} has been one of the prominent methods used to tackle the verification of multi-threaded programs. However, existing model-checking solutions are inefficient while analyzing stateful programming languages, such as the x86 assembly language, due to the solutions' higher level of abstraction. Therefore, the thesis presents xavier, a novel tool-set and a realistic platform for systematically exploring and analyzing the state-space of mainstream concurrent x86 assembly programs, with the aim of detecting bugs via assertion failures. To this end, xavier{} makes two contributions: i) a novel order-sensitivity based Partial Order Reduction algorithm, which efficiently explores the state space of concurrent x86 assembly, ii) an x86 machine-model that can accurately emulate the execution of concurrent x86 assembly, without the need for any translations. We demonstrate the applicability of xavier{} through an evaluation on several classical mutual-exclusion and mainstream benchmarks from the Userspace Read-Copy-Update (URCU) concurrency library, where the benchmarks range from $250-3700$ lines of x86 assembly. Moreover, we demonstrate the effectiveness of xavier{} by reproducing a concurrency issue in the URCU library, which manifests as a result of an assumption violation.

We propose a fully automated and dynamic method for generating likely invariants from multithreaded programs and then leveraging these invariants to infer atomic regions and diagnose concurrency errors in the software code. Although existing methods for dynamic invariant generation perform reasonably well on sequential programs, for multithreaded programs, their effectiveness often reduces dramatically in terms of both the number of invariants that they can generate and the likelihood of them being true invariants. We solve this problem by developing a new dynamic invariant generator, which consists of a new LLVM based code instrumentation tool, an INSPECT based thread interleaving explorer, and a customized inference engine inside Daikon. We have evaluated the resulting system on public domain multithreaded C/C++ benchmarks. Our experiments show that the new method is effective in generating high-quality invariants. Furthermore, the state and transition invariants generated by our new method have been proved useful both in error diagnosis and in identifying likely atomic regions in the concurrent software code. / Master of Science

Nonlinear parametric inverse problems appear in many applications in science and engineering. We focus on diffuse optical tomography (DOT) in medical imaging. DOT aims to recover an unknown image of interest, such as the absorption coefficient in tissue to locate tumors in the body. Using a mathematical (forward) model to predict measurements given a parametrization of the tissue, we minimize the misfit between predicted and actual measurements up to a given noise level. The main computational bottleneck in such inverse problems is the repeated evaluation of this large-scale forward model, which corresponds to solving large linear systems for each source and frequency at each optimization step. Moreover, to efficiently compute derivative information, we need to solve, repeatedly, linear systems with the adjoint for each detector and frequency. As rapid advances in technology allow for large numbers of sources and detectors, these problems become computationally prohibitive. In this thesis, we introduce two methods to drastically reduce this cost. To efficiently implement Newton methods, we extend the use of simultaneous random sources to reduce the number of linear system solves to include simultaneous random detectors. Moreover, we combine simultaneous random sources and detectors with optimized ones that lead to faster convergence and more accurate solutions. We can use reduced order models (ROM) to drastically reduce the size of the linear systems to be solved in each optimization step while still solving the inverse problem accurately. However, the construction of the ROM bases still incurs a substantial cost. We propose to use randomization to drastically reduce the number of large linear solves needed for constructing the global ROM bases without degrading the accuracy of the solution to the inversion problem. We demonstrate the efficiency of these approaches with 2-dimensional and 3-dimensional examples from DOT; however, our methods have the potential to be useful for other applications as well. / Ph. D.