Efficient Interconnection Schemes for VLSI and Parallel Computation

This thesis is primarily concerned with two problems of interconnecting components in VLSI technologies. In the first case, the goal is to construct efficient interconnection networks for general-purpose parallel computers. The second problem is a more specialized problem in the design of VLSI chips, namely multilayer channel routing. In addition, a final part of this thesis provides lower bounds on the area required for VLSI implementations of finite-state machines. This thesis shows that networks based on Leiserson\u27s fat-tree architecture are nearly as good as any network built in a comparable amount of physical space. It shows that these universal networks can efficiently simulate competing networks by means of an appropriate correspondence between network components and efficient algorithms for routing messages on the universal network. In particular, a universal network of area A can simulate competing networks with O(lg^3A) slowdown (in bit-times), using a very simple randomized routing algorithm and simple network components. Alternatively, a packet routing scheme of Leighton, Maggs, and Rao can be used in conjunction with more sophisticated switching components to achieve O(lg^2 A) slowdown. Several other important aspects of universality are also discussed. It is shown that universal networks can be constructed in area linear in the number of processors, so that there is no need to restrict the density of processors in competing networks. Also results are presented for comparisons between networks of different size or with processors of different sizes (as determined by the amount of attached memory). Of particular interest is the fact that a universal network built from sufficiently small processors can simulate (with the slowdown already quoted) any competing network of comparable size regardless of the size of processors in the competing network. In addition, many of the results given do not require the usual assumption of unit wire delay. Finally, though most of the discussion is in the two-dimensional world, the results are shown to apply in three dimensions by way of a simple demonstration of general results on graph layout in three dimensions. The second main problem considered in this thesis is channel routing when many layers of interconnect are available, a scenario that is becoming more and more meaningful as chip fabrication technologies advance. This thesis describes a system MulCh for multilayer channel routing which extends the Chameleon system developed at U. C. Berkeley. Like Chameleon, MulCh divides a multilayer problem into essentially independent subproblems of at most three layers, but unlike Chameleon, MulCh considers the possibility of using partitions comprised of a single layer instead of only partitions of two or three layers. Experimental results show that MulCh often performs better than Chameleon in terms of channel width, total net length, and number of vias. In addition to a description of MulCh as implemented, this thesis provides improved algorithms for subtasks performed by MulCh, thereby indicating potential improvements in the speed and performance of multilayer channel routing. In particular, a linear time algorithm is given for determining the minimum width required for a single-layer channel routing problem, and an algorithm is given for maintaining the density of a collection of nets in logarithmic time per net insertion. The last part of this thesis shows that straightforward techniques for implementing finite-state machines are optimal in the worst case. Specifically, for any s and k, there is a deterministic finite-state machine with s states and k symbols such that any layout algorithm requires (ks lg s) area to lay out its realization. For nondeterministic machines, there is an analogous lower bound of (ks^2) area

Analysis and Optimization of Scientific Applications through Set and Relation Abstractions

Writing high performance code has steadily become more challenging since the design of computing systems has moved toward parallel processors in forms of multi and many-core architectures. This trend has resulted in exceedingly more heterogeneous architectures and programming models. Moreover, the prevalence of distributed systems, especially in fields relying on supercomputers, has caused the programming of such diverse environment more difficulties. To mitigate such challenges, an assortment of tools and programming models have been introduced in the past decade or so. Some efforts focused on the characteristics of the code, such as polyhedral compilers (e.g. Pluto, PPCG, etc.) while others took in consideration the aspects of the application domain and proposed domain specific languages (DSLs). DSLs are developed either in the form of a stand-alone language, like Halide for image processing, or as a part of a general purpose language (e.g., Firedrake- a DSL embedded in Python for solving PDEs using FEM.) called embedded. All these approaches attempt to provide the best input to the underlying common programming models like MPI and OpenMP for distributed and shared memory systems respectively. This dissertation introduces Kaashi, a high-level run-time system, embedded in C++ language, designed to manage memory and execution order of programs with large input data and complex dependencies. Kaashi provides a uniform front-end to multiple back-ends focusing on distributed systems. Kaashi abstractions allows the programmer to define the problem’s data domain as a collection of sets and relations between pairs of such sets. The aforesaid level of abstraction could enable series of optimizations which, otherwise, are very expensive to detect or not feasible at all. Furthermore, Kaashi’s API helps novice programmers to write their code more structurally without getting involved in details of data management and communication

Validation of symbolic expressions in circuit analysis e-learning

Symbolic circuit analysis is a cornerstone of electrical engineering education. Solving a suitable set of selected problems is essential to developing professional skills in the field. Anew method is presented for automatic validation of circuit equations representing a student's intermediate steps in the solving process. Providing this immediate feedback may strongly enhance the training effects. The new method was embedded in a Web-based e-learning system and has proved to be useful in circuit analysis training, both at an introductory level and for more advanced problems in analog electronics

What's the Situation with Intelligent Mesh Generation: A Survey and Perspectives

Intelligent Mesh Generation (IMG) represents a novel and promising field of research, utilizing machine learning techniques to generate meshes. Despite its relative infancy, IMG has significantly broadened the adaptability and practicality of mesh generation techniques, delivering numerous breakthroughs and unveiling potential future pathways. However, a noticeable void exists in the contemporary literature concerning comprehensive surveys of IMG methods. This paper endeavors to fill this gap by providing a systematic and thorough survey of the current IMG landscape. With a focus on 113 preliminary IMG methods, we undertake a meticulous analysis from various angles, encompassing core algorithm techniques and their application scope, agent learning objectives, data types, targeted challenges, as well as advantages and limitations. We have curated and categorized the literature, proposing three unique taxonomies based on key techniques, output mesh unit elements, and relevant input data types. This paper also underscores several promising future research directions and challenges in IMG. To augment reader accessibility, a dedicated IMG project page is available at \url{https://github.com/xzb030/IMG_Survey}

Water flow through tailings dams

Water levels in tailings dams are generally lower than those of standard earth dams. Previously, other authors have shown that embankment geometry and variation in permeability can be responsible for a concave upwards steady state seepage line. These factors are investigated in greater detail using a finite element program to model flow in the saturated portion of the embankment. It is shown that the angle of the upstream slope only has an appreciable effect on the form of the seepage line if the pond is close to the downstream face of the dam. An increasing permeability in the direction of flow and seepage path length are responsible for reducing the height of the seepage line. This effect is demonstrated for both a continuous variation of permeability and a step jump in permeability between the tailings deposit and the dam. Anisotropy of tailings and dam permeability is also investigated. Transient analyses of saturated flow are performed for tailings dams constructed of dry compacted waste. For this case, the seepage line is straight for a constant pond level, and concave upwards for a rising pond and a low dam permeability. The simple computer model also predicts that for a constantly rising pond level, the seepage line advances at a constant rate dependent on the rate of pond rise, and the material properties of the dam. A fully automatic finite element program has been written, combining an adaptive mesh regeneration algorithm and a variable mesh technique. The program is shown to provide both an accurate and precise solution of the free surface problem. A method of automatically generating "square" flow nets by post-processing the finite element data is presented for the first time. Flow nets provide a visual proof of the correctness of the computer model and are a useful aid to other workers

On Causal Equivalence by Tracing in String Rewriting

We introduce proof terms for string rewrite systems and, using these, show that various notions of equivalence on reductions known from the literature can be viewed as different perspectives on the notion of causal equivalence. In particular, we show that permutation equivalence classes (as known from the lambda-calculus and term rewriting) are uniquely represented both by trace graphs (known from physics as causal graphs) and by so-called greedy multistep reductions (as known from algebra). We present effective maps from the former to the latter, topological multi-sorting TM, and vice versa, the proof term algebra [[ ]].Comment: In Proceedings TERMGRAPH 2022, arXiv:2303.1421

Reduced-order modeling of a sliding ring on an elastic rod with incremental potential formulation

Mechanical interactions between rigid rings and flexible cables are widespread in both daily life (hanging clothes) and engineering system (closing a tether net). A reduced-order method for the dynamic analysis of sliding rings on a deformable one-dimensional (1D) rod-like object is proposed. In contrast to discretize the joint rings into multiple nodes and edges for contact detection and numerical simulation, a single point is used to reduce the order of the numerical model. In order to achieve the non-deviation condition between sliding ring and flexible rod, a novel barrier functional is derived based on incremental potential theory, and the tangent frictional interplay is later procured by a lagged dissipative formulation. The proposed barrier functional and the associated frictional functional are $C^{2}$ continuous, hence the nonlinear elastodynamic system can be solved variationally by an implicit time-stepping scheme. The numerical framework is first applied to simple examples where the analytical solutions are available for validation. Then, multiple complex practical engineering examples are considered to showcase the effectiveness of the proposed method. The simplified ring-to-rod interaction model can provide lifelike visual effect for picture animations, and also can support the optimal design for space debris removal system.Comment: 15 pages, 9 figure

Automatic 3D model creation with velocity-based surface deformations

The virtual worlds of Computer Graphics are populated by geometric objects, called models. Researchers have addressed the problem of synthesizing models automatically. Traditional modeling approaches often require a user to guide the synthesis process and to look after the geometry being synthesized, but user attention is expensive, and reducing user interaction is therefore desirable. I present a scheme for the automatic creation of geometry by deforming surfaces. My scheme includes a novel surface representation; it is an explicit representation consisting of points and edges, but it is not a traditional polygonal mesh. The novel surface representation is paired with a resampling policy to control the surface density and its evolution during deformation. The surface deforms with velocities assigned to its points through a set of deformation operators. Deformation operators avoid the manual computation and assignment of velocities, the operators allow a user to interactively assign velocities with minimal effort. Additionally, Petri nets are used to automatically deform a surface by mimicking a user assigning deformation operators. Furthermore, I present an algorithm to translate from the novel surface representations to a polygonal mesh. I demonstrate the utility of my model generation scheme with a gallery of models created automatically. The scheme's surface representation and resampling policy enables a surface to deform without requiring a user to control the deformation; self-intersections and hole creation are automatically prevented. The generated models show that my scheme is well suited to create organic-like models, whose surfaces have smooth transitions between surface features, but can also produce other kinds of models. My scheme allows a user to automatically generate varied instances of richly detailed models with minimal user interaction

An examination and confirmation of a macro theory of conversations through a realization of the protologic Lp by microscopic simulation

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Conversation Theory is a theory of interaction. From interaction (the theory asserts) arises all individuals and all concepts. Interaction, if it is to allow for evolution, must perforce contain conflict, and, if concepts and individuals are to endure, resolution of conflict. Conversation Theory as developed by Pask led to the protologic called Lp which describes the interaction of conceptual entities. Lp contains injunctions as to how entities can and may interact, including how they may conflict and how their conflict may be resolved. Unlike existing software implementations based on Conversation Theory, Lp in its pure form is a logic of process as well as coherence and distinction. The hypothesis is that a low-level simulation of Lp, that of an internal and microscopic level in which topics are influenced by "forces" that are exerted by the topology of the conceptual space, would, in its activation as a dynamic process of appropriate dimension, produce as a result (and hence be a confirmation of) the macroscopically-observed behaviour of the system manifest as conflict and resolution of conflict. Without this confirmation, the relationships between Conversation Theory and Lp remain only proposed; with it, their mutual consistencies and validity as a model of cognition, are affirmed. The background of Conversation Theory and Lp necessary to support the thesis is presented a long with a comparison of other software approaches to related problems. A description of THOUGHTSTICKER, a current embodiment of Lp at the macro level, provides a detailed sense of the Lp operations. Then a computer program (developed to provide a proof by demonstration of the thesis) is described, in which a microscopic simulation of Lp processes confirms the macroscopic behaviour predicted by Conversation Theory. Conversation Theory thereby gains support f or its use as a valid observer's language for every-day experience owing to this confirmation and its protologic as a basis for psychological phenomena in the interaction of conceptual entities of mind