55 research outputs found
Efficient algorithms for reconfiguration in VLSI/WSI arrays
The issue of developing efficient algorithms for reconfiguring processor arrays in the presence of faulty processors and fixed hardware resources is discussed. The models discussed consist of a set of identical processors embedded in a flexible interconnection structure that is configured in the form of a rectangular grid. An array grid model based on single-track switches is considered. An efficient polynomial time algorithm is proposed for determining feasible reconfigurations for an array with a given distribution of faulty processors. In the process, it is shown that the set of conditions in the reconfigurability theorem is not necessary. A polynomial time algorithm is developed for finding feasible reconfigurations in an augmented single-track model and in array grid models with multiple-track switche
Modelling and quantification of structural uncertainties in petroleum reservoirs assisted by a hybrid cartesian cut cell/enriched multipoint flux approximation approach
Efficient and profitable oil production is subject to make reliable predictions about
reservoir performance. However, restricted knowledge about reservoir distributed
properties and reservoir structure calls for History Matching in which the reservoir
model is calibrated to emulate the field observed history. Such an inverse problem
yields multiple history-matched models which might result in different predictions of
reservoir performance. Uncertainty Quantification restricts the raised model
uncertainties and boosts the model reliability for the forecasts of future reservoir
behaviour. Conventional approaches of Uncertainty Quantification ignore large scale
uncertainties related to reservoir structure, while structural uncertainties can influence
the reservoir forecasts more intensely compared with petrophysical uncertainty.
What makes the quantification of structural uncertainty impracticable is the need for
global regridding at each step of History Matching process. To resolve this obstacle, we
develop an efficient methodology based on Cartesian Cut Cell Method which decouples
the model from its representation onto the grid and allows uncertain structures to be
varied as a part of History Matching process. Reduced numerical accuracy due to cell
degeneracies in the vicinity of geological structures is adequately compensated with an
enhanced scheme of class Locally Conservative Flux Continuous Methods (Extended
Enriched Multipoint Flux Approximation Method abbreviated to extended EMPFA).
The robustness and consistency of proposed Hybrid Cartesian Cut Cell/extended
EMPFA approach are demonstrated in terms of true representation of geological
structures influence on flow behaviour. In this research, the general framework of
Uncertainty Quantification is extended and well-equipped by proposed approach to
tackle uncertainties of different structures such as reservoir horizons, bedding layers,
faults and pinchouts. Significant improvements in the quality of reservoir recovery
forecasts and reservoir volume estimation are presented for synthetic models of
uncertain structures. Also this thesis provides a comparative study of structural
uncertainty influence on reservoir forecasts among various geological structures
Combinatorics and geometry of finite and infinite squaregraphs
Squaregraphs were originally defined as finite plane graphs in which all
inner faces are quadrilaterals (i.e., 4-cycles) and all inner vertices (i.e.,
the vertices not incident with the outer face) have degrees larger than three.
The planar dual of a finite squaregraph is determined by a triangle-free chord
diagram of the unit disk, which could alternatively be viewed as a
triangle-free line arrangement in the hyperbolic plane. This representation
carries over to infinite plane graphs with finite vertex degrees in which the
balls are finite squaregraphs. Algebraically, finite squaregraphs are median
graphs for which the duals are finite circular split systems. Hence
squaregraphs are at the crosspoint of two dualities, an algebraic and a
geometric one, and thus lend themselves to several combinatorial
interpretations and structural characterizations. With these and the
5-colorability theorem for circle graphs at hand, we prove that every
squaregraph can be isometrically embedded into the Cartesian product of five
trees. This embedding result can also be extended to the infinite case without
reference to an embedding in the plane and without any cardinality restriction
when formulated for median graphs free of cubes and further finite
obstructions. Further, we exhibit a class of squaregraphs that can be embedded
into the product of three trees and we characterize those squaregraphs that are
embeddable into the product of just two trees. Finally, finite squaregraphs
enjoy a number of algorithmic features that do not extend to arbitrary median
graphs. For instance, we show that median-generating sets of finite
squaregraphs can be computed in polynomial time, whereas, not unexpectedly, the
corresponding problem for median graphs turns out to be NP-hard.Comment: 46 pages, 14 figure
Geometric Path-Planning Algorithm in Cluttered 2D Environments Using Convex Hulls
Routing or path planning is the problem of finding a collision-free path in an environment usually scattered with multiple objects. Finding the shortest route in a planar (2D) or spatial (3D) environment has a variety of applications such as robot motion planning, navigating autonomous vehicles, routing of cables, wires, and harnesses in vehicles, routing of pipes in chemical process plants, etc. The problem often times is decomposed into two main sub-problems: modeling and representation of the workspace geometrically and optimization of the path. Geometric modeling and representation of the workspace are paramount in any path planning problem since it builds the data structures and provides the means for solving the optimization problem. The optimization aspect of the path planning involves satisfying some constraints, the most important of which is to avoid intersections with the interior of any object and optimizing one or more criteria. The most common criterion in path planning problems is to minimize the length of the path between a source and a destination point of the workspace while other criteria such as minimizing the number of links or curves could also be taken into account. Planar path planning is mainly about modeling the workspace of the problem as a collision-free graph. The graph is, later on, searched for the optimal path using network optimization techniques such as branch-and-bound or search algorithms such as Dijkstra\u27s. Previous methods developed to construct the collision-free graph explore the entire workspace of the problem which usually results in some unnecessary information that has no value but to increase the time complexity of the algorithm, hence, affecting the efficiency significantly. For example, the fastest known algorithm to construct the visibility graph, which is the most common method of modeling the collision-free space, in a workspace with a total of n vertices has a time complexity of order O(n2). In this research, first, the 2D workspace of the problem is modeled using the tessellated format of the objects in a CAD software which facilitates handling of any free-form object. Then, an algorithm is developed to construct the collision-free graph of the workspace using the convex hulls of the intersecting obstacles. The proposed algorithm focuses only on a portion of the workspace involved in the straight line connecting the source and destination points. Considering the worst case that all the objects of the workspace are intersecting, the algorithm yields a time complexity of O(nlog(n/f)), with n being the total number of vertices and f being the number of objects. The collision-free graph is later searched for the shortest path between the two given nodes using a search algorithm known as Dijkstra\u27s
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