Multilevel Domain Decomposition Algorithms for Monolithic Fluid-Structure Interaction Problems with Application to Haemodynamics

Finite element techniques for solving the problem of fluid-structure interaction of an elastic solid material in a laminar incompressible viscous flow are described. The mathematical problem consists of the Navier-Stokes equations in the Arbitrary Lagrangian-Eulerian formulation coupled with a non-linear structure model, considering the problem as one continuum. The coupling between the structure and the fluid is enforced inside a monolithic framework which computes simultaneously for the fluid and the structure unknowns within a unique solver. We used the well-known Crouzeix-Raviart finite element pair for discretization in space and the method of lines for discretization in time. A stability result using the Backward-Euler time-stepping scheme for both fluid and solid part and the finite element method for the space discretization has been proved. The resulting linear system has been solved by multilevel domain decomposition techniques. Our strategy is to solve several local subproblems over subdomain patches using the Schur-complement or GMRES smoother within a multigrid iterative solver. For validation and evaluation of the accuracy of the proposed methodology, we present corresponding results for a set of two FSI benchmark configurations which describe the self-induced elastic deformation of a beam attached to a cylinder in a laminar channel flow, allowing stationary as well as periodically oscillating deformations, and for a benchmark proposed by COMSOL multiphysics where a narrow vertical structure attached to the bottom wall of a channel bends under the force due to both viscous drag and pressure. Then, as an example of fluid-structure interaction in biomedical problems, we considered the academic numerical test which consists in simulating the pressure wave propagation through a straight compliant vessel. All the tests show the applicability and the numerical efficiency of our approach to both two-dimensional and three-dimensional problems.

Management and routing algorithms for ad-hoc and sensor networks

Large scale wireless adhoc networks of computers, sensors, PDAs etc. (i.e. nodes) are revolutionizing connectivity and leading to a paradigm shift from centralized systems to highly distributed and dynamic environments. An example of adhoc networks are sensor networks, which are usually composed by small units able to sense and transmit to a sink elementary data which are successively processed by an external machine. Recent improvements in the memory and computational power of sensors, together with the reduction of energy consumptions, are rapidly changing the potential of such systems, moving the attention towards datacentric sensor networks. A plethora of routing and data management algorithms have been proposed for the network path discovery ranging from broadcasting/floodingbased approaches to those using global positioning systems (GPS). We studied WGrid, a novel decentralized infrastructure that organizes wireless devices in an adhoc manner, where each node has one or more virtual coordinates through which both message routing and data management occur without reliance on either flooding/broadcasting operations or GPS. The resulting adhoc network does not suffer from the deadend problem, which happens in geographicbased routing when a node is unable to locate a neighbor closer to the destination than itself. WGrid allow multidimensional data management capability since nodes' virtual coordinates can act as a distributed database without needing neither special implementation or reorganization. Any kind of data (both single and multidimensional) can be distributed, stored and managed. We will show how a location service can be easily implemented so that any search is reduced to a simple query, like for any other data type. WGrid has then been extended by adopting a replication methodology. We called the resulting algorithm WRGrid. Just like WGrid, WRGrid acts as a distributed database without needing neither special implementation nor reorganization and any kind of data can be distributed, stored and managed. We have evaluated the benefits of replication on data management, finding out, from experimental results, that it can halve the average number of hops in the network. The direct consequence of this fact are a significant improvement on energy consumption and a workload balancing among sensors (number of messages routed by each node). Finally, thanks to the replications, whose number can be arbitrarily chosen, the resulting sensor network can face sensors disconnections/connections, due to failures of sensors, without data loss. Another extension to {WGrid} is {W*Grid} which extends it by strongly improving network recovery performance from link and/or device failures that may happen due to crashes or battery exhaustion of devices or to temporary obstacles. W*Grid guarantees, by construction, at least two disjoint paths between each couple of nodes. This implies that the recovery in W*Grid occurs without broadcasting transmissions and guaranteeing robustness while drastically reducing the energy consumption. An extensive number of simulations shows the efficiency, robustness and traffic road of resulting networks under several scenarios of device density and of number of coordinates. Performance analysis have been compared to existent algorithms in order to validate the results.

Design and Performance Evaluation of Network-on-Chip Communication Protocols and Architectures

The scale down of transistor technology allows microelectronics manufacturers such as Intel and IBM to build always more sophisticated systems on a single microchip. The classical interconnection solutions based on shared buses or direct connections between the modules of the chip are becoming obsolete as they struggle to sustain the increasing tight bandwidth and latency constraints that these systems demand. The most promising solution for the future chip interconnects are the Networks on Chip (NoC). NoCs are network composed by routers and channels used to inter- connect the different components installed on the single microchip. Examples of advanced processors based on NoC interconnects are the IBM Cell processor, composed by eight CPUs that is installed on the Sony Playstation III and the Intel Teraflops pro ject composed by 80 independent (simple) microprocessors. On chip integration is becoming popular not only in the Chip Multi Processor (CMP) research area but also in the wider and more heterogeneous world of Systems on Chip (SoC). SoC comprehend all the electronic devices that surround us such as cell-phones, smart-phones, house embedded systems, automotive systems, set-top boxes etc... SoC manufacturers such as ST Microelectronics , Samsung, Philips and also Universities such as Bologna University, M.I.T., Berkeley and more are all proposing proprietary frameworks based on NoC interconnects. These frameworks help engineers in the switch of design methodology and speed up the development of new NoC-based systems on chip. In this Thesis we propose an introduction of CMP and SoC interconnection networks. Then focusing on SoC systems we propose: • a detailed analysis based on simulation of the Spidergon NoC, a ST Microelectronics solution for SoC interconnects. The Spidergon NoC differs from many classical solutions inherited from the parallel computing world. Here we propose a detailed analysis of this NoC topology and routing algorithms. Furthermore we propose aEqualized a new routing algorithm designed to optimize the use of the resources of the network while also increasing its performance; • a methodology flow based on modified publicly available tools that combined can be used to design, model and analyze any kind of System on Chip; • a detailed analysis of a ST Microelectronics-proprietary transport-level protocol that the author of this Thesis helped developing; • a simulation-based comprehensive comparison of different network interface designs proposed by the author and the researchers at AST lab, in order to integrate shared-memory and message-passing based components on a single System on Chip; • a powerful and flexible solution to address the time closure exception issue in the design of synchronous Networks on Chip. Our solution is based on relay stations repeaters and allows to reduce the power and area demands of NoC interconnects while also reducing its buffer needs; • a solution to simplify the design of the NoC by also increasing their performance and reducing their power and area consumption. We propose to replace complex and slow virtual channel-based routers with multiple and flexible small Multi Plane ones. This solution allows us to reduce the area and power dissipation of any NoC while also increasing its performance especially when the resources are reduced. This Thesis has been written in collaboration with the Advanced System Technology laboratory in Grenoble France, and the Computer Science Department at Columbia University in the city of New York.

Graph algorithms for bioinformatics

Biological data are inherently interconnected: protein sequences are connected to their annotations, the annotations are structured into ontologies, and so on. While protein-protein interactions are already represented by graphs, in this work I am presenting how a graph structure can be used to enrich the annotation of protein sequences thanks to algorithms that analyze the graph topology. We also describe a novel solution to restrict the data generation needed for building such a graph, thanks to constraints on the data and dynamic programming. The proposed algorithm ideally improves the generation time by a factor of 5. The graph representation is then exploited to build a comprehensive database, thanks to the rising technology of graph databases. While graph databases are widely used for other kind of data, from Twitter tweets to recommendation systems, their application to bioinformatics is new. A graph database is proposed, with a structure that can be easily expanded and queried.

Tensor-Train decomposition for image classification problems

In these last years a great effort has been put in the development of new techniques for automatic object classification, also due to the consequences in many applications such as medical imaging or driverless cars. To this end, several mathematical models have been developed from logistic regression to neural networks. A crucial aspect of these so called classification algorithms is the use of algebraic tools to represent and approximate the input data. In this thesis, we examine two different models for image classification based on a particular tensor decomposition named Tensor-Train (TT) decomposition. The use of tensor approaches preserves the multidimensional structure of the data and the neighboring relations among pixels. Furthermore the Tensor-Train, differently from other tensor decompositions, does not suffer from the curse of dimensionality making it an extremely powerful strategy when dealing with high-dimensional data. It also allows data compression when combined with truncation strategies that reduce memory requirements without spoiling classification performance. The first model we propose is based on a direct decomposition of the database by means of the TT decomposition to find basis vectors used to classify a new object. The second model is a tensor dictionary learning model, based on the TT decomposition where the terms of the decomposition are estimated using a proximal alternating linearized minimization algorithm with a spectral stepsize.

Exact and heuristic algorithms for the integrated planning of multi-energy systems

The aim of this thesis is to present exact and heuristic algorithms for the integrated planning of multi-energy systems. The idea is to disaggregate the energy system, starting first with its core the Central Energy System, and then to proceed towards the Decentral part. Therefore, a mathematical model for the generation expansion operations to optimize the performance of a Central Energy System system is first proposed. To ensure that the proposed generation operations are compatible with the network, some extensions of the existing network are considered as well. All these decisions are evaluated both from an economic viewpoint and from an environmental perspective, as specific constraints related to greenhouse gases emissions are imposed in the formulation. Then, the thesis presents an optimization model for solar organic Rankine cycle in the context of transactive energy trading. In this study, the impact that this technology can have on the peer-to-peer trading application in renewable based community microgrids is inspected. Here the consumer becomes a prosumer and engages actively in virtual trading with other prosumers at the distribution system level. Moreover, there is an investigation of how different technological parameters of the solar Organic Rankine Cycle may affect the final solution. Finally, the thesis introduces a tactical optimization model for the maintenance operations’ scheduling phase of a Combined Heat and Power plant. Specifically, two types of cleaning operations are considered, i.e., online cleaning and offline cleaning. Furthermore, a piecewise linear representation of the electric efficiency variation curve is included. Given the challenge of solving the tactical management model, a heuristic algorithm is proposed. The heuristic works by solving the daily operational production scheduling problem, based on the final consumer’s demand and on the electricity prices. The aggregate information from the operational problem is used to derive maintenance decisions at a tactical level.