Luis Silveira - Academia.edu (original) (raw)

Papers by Luis Silveira

Research paper thumbnail of Session details: Circuit performance under parameter variation

Design Automation Conference, Jun 13, 2005

Research paper thumbnail of Poor man's TBR: a simple model reduction scheme

Design, Automation, and Test in Europe, Feb 16, 2004

Abstract—This paper presents a model reduction algorithm motivated by a connection between freque... more Abstract—This paper presents a model reduction algorithm motivated by a connection between frequency-domain projection methods and approximation of truncated balanced realizations. The method is computationally simple to implement, has near-op-timal error ...

Research paper thumbnail of Learning the dynamics of realistic models of C. elegans nervous system with recurrent neural networks

Scientific Reports

Given the inherent complexity of the human nervous system, insight into the dynamics of brain act... more Given the inherent complexity of the human nervous system, insight into the dynamics of brain activity can be gained from studying smaller and simpler organisms. While some of the potential target organisms are simple enough that their behavioural and structural biology might be well-known and understood, others might still lead to computationally intractable models that require extensive resources to simulate. Since such organisms are frequently only acting as proxies to further our understanding of underlying phenomena or functionality, often one is not interested in the detailed evolution of every single neuron in the system. Instead, it is sufficient to observe the subset of neurons that capture the effect that the profound nonlinearities of the neuronal system have in response to different stimuli. In this paper, we consider the well-known nematode Caenorhabditis elegans and seek to investigate the possibility of generating lower complexity models that capture the system’s dyna...

Research paper thumbnail of Modelling Neuronal Behaviour with Time Series Regression: Recurrent Neural Networks on C. Elegans Data

arXiv (Cornell University), Jul 1, 2021

Given the inner complexity of the human nervous system, insight into the dynamics of brain activi... more Given the inner complexity of the human nervous system, insight into the dynamics of brain activity can be gained from understanding smaller and simpler organisms, such as the nematode C. Elegans. The behavioural and structural biology of these organisms is well-known, making them prime candidates for benchmarking modelling and simulation techniques. In these complex neuronal collections, classical, white-box modelling techniques based on intrinsic structural or behavioural information are either unable to capture the profound nonlinearities of the neuronal response to different stimuli or generate extremely complex models, which are computationally intractable. In this paper we show how the nervous system of C. Elegans can be modelled and simulated with data-driven models using different neural network architectures. Specifically, we target the use of state of the art recurrent neural networks architectures such as LSTMs and GRUs and compare these architectures in terms of their properties and their accuracy as well as the complexity of the resulting models. We show that GRU models with a hidden layer size of 4 units are able to accurately reproduce with high accuracy the system's response to very different stimuli. Preprint. Under review.

Research paper thumbnail of Efficient Model Reduction of Myelinated Compartments as Port-Hamiltonian Systems

Scientific Computing in Electrical Engineering, 2021

The information is transmitted in neurons through axons, many of whom have myelin-covered section... more The information is transmitted in neurons through axons, many of whom have myelin-covered sections, whose main purpose is to increase the speed of electrical signal transmission. Modeling the myelinated axons in a realistic way, by maintaining the physical meaning of components may lead to complex systems, described by high-dimensional systems of PDEs, whose solution is computationally demanding. Analysis of larger neuronal circuits including multiple myelinated axons therefore requires the generation of equivalent low-order models to control complexity. Such models must preserve the physical interpretation and properties of the original system including its passivity and stability. The axons' port-based structure makes them suitable to be modeled as port-Hamiltonian systems. This paper uses a structure-preserving reduction method for port-Hamiltonian systems to reduce the description of a myelinated compartment into a model with comparable accuracy with the previously used vector fitting technique. The reduced system is synthesized into an equivalent passive circuit with no controlled sources and only positive elements, amenable for inclusion in standard neuronal simulators.

Research paper thumbnail of Erratum to: VLSI: Systems on a Chip

VLSI: Systems on a Chip, 2017

Research paper thumbnail of 5 Post-processing methods for passivity enforcement

System- and Data-Driven Methods and Algorithms, 2021

Many physical systems are passive (or dissipative): they are unable to generate energy on their o... more Many physical systems are passive (or dissipative): they are unable to generate energy on their own, but they can store energy in some form while exchanging power with the surrounding environment. This chapter describes the most prominent approaches for ensuring that Reduced Order Models are passive, so that their mathematical representation satisfies an appropriate dissipativity condition. The main focus is on Linear and Time-Invariant (LTI) systems in state-space form. Different conditions for testing passivity of a given LTI model are discussed, including Linear Matrix Inequalities (LMIs), Frequency-Domain Inequalities, and spectral conditions on associated Hamiltonian matrices. Then we describe common approaches for perturbing a given non-passive system to enforce its passivity. Various examples from electronic applications are used to demonstrate both theory and algorithm performance.

Research paper thumbnail of 1 Model order reduction: basic concepts and notation

System- and Data-Driven Methods and Algorithms, 2021

This is the first chapter of a three-volume series dedicated to theory and application of Model O... more This is the first chapter of a three-volume series dedicated to theory and application of Model Order Reduction (MOR). We motivate and introduce the basic concepts and notation, with reference to the two main cultural approaches to MOR: the system-theoretic approach employing state-space models and transfer function concepts (Volume 1), and the numerical analysis approach as applied to partial differential operators (Volume 2), for which projection and approximation in suitable function spaces provide a rich set of tools for MOR. These two approaches are complementary but share the main objective of simplifying numerical computations while retaining accuracy. Despite the sometimes different adopted language and notation, they also share the main ideas and key concepts, which are briefly summarized in this chapter. The material is presented so that all chapters in this three-volume series are put into context, by highlighting the specific problems that they address. An overview of all MOR applications in Volume 3 is also provided.

Research paper thumbnail of A Microprocessor Implementation of a Self-Tuning Controller

Adaptive Systems in Control and Signal Processing 1986, 1987

The software implementation of a self-tuning controller in a 16 bit microprocessor (INTEL 8086) i... more The software implementation of a self-tuning controller in a 16 bit microprocessor (INTEL 8086) is discribed and discussed at the light of the experimental results obtained. The algorithm used combines generalized m nimum variance servo-control, the UD implementation of least-squares estimation and a variable forgetting factor. Problems that confront the implementation of adaptive controllers in a 16 bit environment with fixed point arithmetic (16+16 bits) and limited available memory are discussed. A series of real time experimental case-studies are presented in order to evaluate the implementation done. The aplication of the self-tuning controller to a thermal diffusion process is ilustrated.

Research paper thumbnail of Parameterized Model Order Reduction

Mathematics in Industry, 2015

DOI to the publisher's website. • The final author version and the galley proof are versions of t... more DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:

Research paper thumbnail of A modified envelope-following approach to clocked analog circuit simulation

1991 IEEE International Conference on Computer-Aided Design Digest of Technical Papers

Research paper thumbnail of A probabilistic approach for RT-level power modeling

ICECS'99. Proceedings of ICECS '99. 6th IEEE International Conference on Electronics, Circuits and Systems (Cat. No.99EX357)

We propose a method for register-transfer level (RTL) power modeling. The switched capacitance an... more We propose a method for register-transfer level (RTL) power modeling. The switched capacitance and switching probability of each output of a functional module are modeled by formulas that are a function of the module's inputs probabilities. These formulas are computed beforehand for each module using the polynomial simulation scheme, and stored in the module library. The switched capacitance (and thus power) for each instance of a module in the circuit can then be efficiently evaluated for its specific input probabilities. The switching probabilities at the outputs of each module can be computed in a similar manner, thus providing a means of propagating the switching probabilities through the circuit described at the RT level. We provide a set of experimental results that show that this method provides estimates close to the logic-level estimates, but is orders of magnitude faster.

Research paper thumbnail of SIMLAB programmer's guide

Supported by the National Science Foundation. MIP 91-17724 A. Lumsdaine, M. Silveira, J. White.

Research paper thumbnail of Direct computation of reduced-order models for circuit simulation of 3-D interconnect structures

This paper describes an accurate and efficient approach for using a modification of the iterative... more This paper describes an accurate and efficient approach for using a modification of the iterative method in the 3-D magnetoquasistatics-based field solver FASTHENRY to compute reduced-order models of frequency-dependent impedance matrices. The reduced-order models can then be used in a circuit simulator to perform coupled circuit-packaging analysis

Research paper thumbnail of Efficient techniques for accurate extraction and modeling of substrate coupling in mixed-signal IC's

Proceedings of the conference on Design, automation and test in Europe - DATE '99, 1999

Accurate modeling of noise coupling effects due to crosstalk via the substrate is an increasingly... more Accurate modeling of noise coupling effects due to crosstalk via the substrate is an increasingly important concern for the design and verification of mixed analogdigital systems. In this paper we present a technique to accelerate the model computation using BEM methods that can be used for accurate and efficient extraction of substrate coupling parameters in mixed-signal designs.

Research paper thumbnail of Robust rational function approximation algorithm for model generation

Proceedings 1999 Design Automation Conference (Cat. No. 99CH36361)

The problem of computing rational function approximations to tabulated frequency data is of param... more The problem of computing rational function approximations to tabulated frequency data is of paramount importance in the modeling arena. In this paper we present a method for generating a state space model from tabular data in the frequency domain that solves some of the numerical difficulties associated with the traditional fitting techniques used in linear least squares approximations. An extension to the MIMO case is also derived.

Research paper thumbnail of Library compatible variational delay computation

IFIP International Federation for Information Processing, 2008

With technology steadily progressing into nanometer dimensions, precise control over all aspects ... more With technology steadily progressing into nanometer dimensions, precise control over all aspects of the fabrication process becomes an area of increasing concern. Process variations have immediate impact on circuit performance and behavior and standard design and signoff methodologies have to account for such variability. In this context, timing verification, already a challenging task due to the sheer complexity of todays designs, becomes an increasingly difficult problem. Statistical static timing analysis has been proposed as a solution to this problem, but most of the work has focused in the development of timing engines for computing delay propagation. Such tools rely on the availability of delay formulas accounting for both cell and interconnect delay that take into account unpredictable variability effects. In this paper, we concentrate on the impact of interconnect on delay and propose an extension to the standard modeling strategies that is variation-aware and compatible with such statistical engines. Our approach, based on a specific type of perturbation analysis, allows for the analytical computation of the quantities needed for statistical delay propagation. We also show how perturbation analysis can be performed when only the standard delay table lookup models are available for the standard cells. This makes the proposed approach compatible with existing timing analysis frameworks. Results from applying our proposed modeling strategy to computing delays and slews in several instances accurately match similar results obtained using electrical level simulation.

Research paper thumbnail of Efficient Representation and Analysis of Power Grids

2008 Design, Automation and Test in Europe, 2008

Modern deep sub-micron ULSI designs with hundreds of millions of devices require huge grids for p... more Modern deep sub-micron ULSI designs with hundreds of millions of devices require huge grids for power distribution. Such grids, operating with increasingly low-power voltages, are a design limiting factor and accurate analysis of their behavior is of paramount importance as any voltage drops can seriously impact performance or functionality. As power grid models have millions of unknowns, highly optimized special purpose simulation tools are required to handle the time and memory complexity of solving for their dynamic behavior. In this work, we propose a hierarchical matrix representation of the power grid model that is both space and time efficient. With this representation, reduced storage matrix factors are efficiently computed and applied in the analysis at every time-step of the simulation. Results show an almost linear complexity growth, namely O(nlog a (n)), for some small constant a, in both space and time, when using this matrix representation. Comparisons of our academic implementation with production-quality code proves this method to be very efficient when dealing with the simulation of large power grid models

Research paper thumbnail of Coupled Circuit-Interconnect Modeling and Simulation

VLSI: Integrated Systems on Silicon, 1997

In this paper we discuss generating low order models for efficient coupled circuitinterconnect si... more In this paper we discuss generating low order models for efficient coupled circuitinterconnect simulation. The ever increasing speeds and shrinking feature sizes that are typical of state of the art integrated circuits designs have made coupling due to interconnect and packaging a very important, sometimes dominant, factor in system performance. The ability to efficiently perform coupled circuit-interconnect simulation before fabrication is essential in order to detect signal degradation due to delays or crosstalk. We first discuss methods of generating models for both two and three dimensional interconnect and then present a general, guaranteed-stable, model order reduction technique to reduce the order of the interconnect models.

Research paper thumbnail of Order reduction techniques for coupled multi-domain electromagnetic based models

This work presents a comprehensive flow able to efficiently generate reduced order models for rea... more This work presents a comprehensive flow able to efficiently generate reduced order models for realistic, hierarchy aware, Electromagnetic (EM) based models. Knowledge of the structure of the problem is explicitly exploited using domain partitioning and novel electromagnetic connector modeling techniques to generate a hierarchically coupled representation. This enables the efficient use of structure preserving block model order reduction techniques to generate block-wise compressed models that satisfy overall requirements, and provide cheap evaluation and simulation accurate approximations of the complete EM behaviour.

Research paper thumbnail of Session details: Circuit performance under parameter variation

Design Automation Conference, Jun 13, 2005

Research paper thumbnail of Poor man's TBR: a simple model reduction scheme

Design, Automation, and Test in Europe, Feb 16, 2004

Abstract—This paper presents a model reduction algorithm motivated by a connection between freque... more Abstract—This paper presents a model reduction algorithm motivated by a connection between frequency-domain projection methods and approximation of truncated balanced realizations. The method is computationally simple to implement, has near-op-timal error ...

Research paper thumbnail of Learning the dynamics of realistic models of C. elegans nervous system with recurrent neural networks

Scientific Reports

Given the inherent complexity of the human nervous system, insight into the dynamics of brain act... more Given the inherent complexity of the human nervous system, insight into the dynamics of brain activity can be gained from studying smaller and simpler organisms. While some of the potential target organisms are simple enough that their behavioural and structural biology might be well-known and understood, others might still lead to computationally intractable models that require extensive resources to simulate. Since such organisms are frequently only acting as proxies to further our understanding of underlying phenomena or functionality, often one is not interested in the detailed evolution of every single neuron in the system. Instead, it is sufficient to observe the subset of neurons that capture the effect that the profound nonlinearities of the neuronal system have in response to different stimuli. In this paper, we consider the well-known nematode Caenorhabditis elegans and seek to investigate the possibility of generating lower complexity models that capture the system’s dyna...

Research paper thumbnail of Modelling Neuronal Behaviour with Time Series Regression: Recurrent Neural Networks on C. Elegans Data

arXiv (Cornell University), Jul 1, 2021

Given the inner complexity of the human nervous system, insight into the dynamics of brain activi... more Given the inner complexity of the human nervous system, insight into the dynamics of brain activity can be gained from understanding smaller and simpler organisms, such as the nematode C. Elegans. The behavioural and structural biology of these organisms is well-known, making them prime candidates for benchmarking modelling and simulation techniques. In these complex neuronal collections, classical, white-box modelling techniques based on intrinsic structural or behavioural information are either unable to capture the profound nonlinearities of the neuronal response to different stimuli or generate extremely complex models, which are computationally intractable. In this paper we show how the nervous system of C. Elegans can be modelled and simulated with data-driven models using different neural network architectures. Specifically, we target the use of state of the art recurrent neural networks architectures such as LSTMs and GRUs and compare these architectures in terms of their properties and their accuracy as well as the complexity of the resulting models. We show that GRU models with a hidden layer size of 4 units are able to accurately reproduce with high accuracy the system's response to very different stimuli. Preprint. Under review.

Research paper thumbnail of Efficient Model Reduction of Myelinated Compartments as Port-Hamiltonian Systems

Scientific Computing in Electrical Engineering, 2021

The information is transmitted in neurons through axons, many of whom have myelin-covered section... more The information is transmitted in neurons through axons, many of whom have myelin-covered sections, whose main purpose is to increase the speed of electrical signal transmission. Modeling the myelinated axons in a realistic way, by maintaining the physical meaning of components may lead to complex systems, described by high-dimensional systems of PDEs, whose solution is computationally demanding. Analysis of larger neuronal circuits including multiple myelinated axons therefore requires the generation of equivalent low-order models to control complexity. Such models must preserve the physical interpretation and properties of the original system including its passivity and stability. The axons' port-based structure makes them suitable to be modeled as port-Hamiltonian systems. This paper uses a structure-preserving reduction method for port-Hamiltonian systems to reduce the description of a myelinated compartment into a model with comparable accuracy with the previously used vector fitting technique. The reduced system is synthesized into an equivalent passive circuit with no controlled sources and only positive elements, amenable for inclusion in standard neuronal simulators.

Research paper thumbnail of Erratum to: VLSI: Systems on a Chip

VLSI: Systems on a Chip, 2017

Research paper thumbnail of 5 Post-processing methods for passivity enforcement

System- and Data-Driven Methods and Algorithms, 2021

Many physical systems are passive (or dissipative): they are unable to generate energy on their o... more Many physical systems are passive (or dissipative): they are unable to generate energy on their own, but they can store energy in some form while exchanging power with the surrounding environment. This chapter describes the most prominent approaches for ensuring that Reduced Order Models are passive, so that their mathematical representation satisfies an appropriate dissipativity condition. The main focus is on Linear and Time-Invariant (LTI) systems in state-space form. Different conditions for testing passivity of a given LTI model are discussed, including Linear Matrix Inequalities (LMIs), Frequency-Domain Inequalities, and spectral conditions on associated Hamiltonian matrices. Then we describe common approaches for perturbing a given non-passive system to enforce its passivity. Various examples from electronic applications are used to demonstrate both theory and algorithm performance.

Research paper thumbnail of 1 Model order reduction: basic concepts and notation

System- and Data-Driven Methods and Algorithms, 2021

This is the first chapter of a three-volume series dedicated to theory and application of Model O... more This is the first chapter of a three-volume series dedicated to theory and application of Model Order Reduction (MOR). We motivate and introduce the basic concepts and notation, with reference to the two main cultural approaches to MOR: the system-theoretic approach employing state-space models and transfer function concepts (Volume 1), and the numerical analysis approach as applied to partial differential operators (Volume 2), for which projection and approximation in suitable function spaces provide a rich set of tools for MOR. These two approaches are complementary but share the main objective of simplifying numerical computations while retaining accuracy. Despite the sometimes different adopted language and notation, they also share the main ideas and key concepts, which are briefly summarized in this chapter. The material is presented so that all chapters in this three-volume series are put into context, by highlighting the specific problems that they address. An overview of all MOR applications in Volume 3 is also provided.

Research paper thumbnail of A Microprocessor Implementation of a Self-Tuning Controller

Adaptive Systems in Control and Signal Processing 1986, 1987

The software implementation of a self-tuning controller in a 16 bit microprocessor (INTEL 8086) i... more The software implementation of a self-tuning controller in a 16 bit microprocessor (INTEL 8086) is discribed and discussed at the light of the experimental results obtained. The algorithm used combines generalized m nimum variance servo-control, the UD implementation of least-squares estimation and a variable forgetting factor. Problems that confront the implementation of adaptive controllers in a 16 bit environment with fixed point arithmetic (16+16 bits) and limited available memory are discussed. A series of real time experimental case-studies are presented in order to evaluate the implementation done. The aplication of the self-tuning controller to a thermal diffusion process is ilustrated.

Research paper thumbnail of Parameterized Model Order Reduction

Mathematics in Industry, 2015

DOI to the publisher's website. • The final author version and the galley proof are versions of t... more DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:

Research paper thumbnail of A modified envelope-following approach to clocked analog circuit simulation

1991 IEEE International Conference on Computer-Aided Design Digest of Technical Papers

Research paper thumbnail of A probabilistic approach for RT-level power modeling

ICECS'99. Proceedings of ICECS '99. 6th IEEE International Conference on Electronics, Circuits and Systems (Cat. No.99EX357)

We propose a method for register-transfer level (RTL) power modeling. The switched capacitance an... more We propose a method for register-transfer level (RTL) power modeling. The switched capacitance and switching probability of each output of a functional module are modeled by formulas that are a function of the module's inputs probabilities. These formulas are computed beforehand for each module using the polynomial simulation scheme, and stored in the module library. The switched capacitance (and thus power) for each instance of a module in the circuit can then be efficiently evaluated for its specific input probabilities. The switching probabilities at the outputs of each module can be computed in a similar manner, thus providing a means of propagating the switching probabilities through the circuit described at the RT level. We provide a set of experimental results that show that this method provides estimates close to the logic-level estimates, but is orders of magnitude faster.

Research paper thumbnail of SIMLAB programmer's guide

Supported by the National Science Foundation. MIP 91-17724 A. Lumsdaine, M. Silveira, J. White.

Research paper thumbnail of Direct computation of reduced-order models for circuit simulation of 3-D interconnect structures

This paper describes an accurate and efficient approach for using a modification of the iterative... more This paper describes an accurate and efficient approach for using a modification of the iterative method in the 3-D magnetoquasistatics-based field solver FASTHENRY to compute reduced-order models of frequency-dependent impedance matrices. The reduced-order models can then be used in a circuit simulator to perform coupled circuit-packaging analysis

Research paper thumbnail of Efficient techniques for accurate extraction and modeling of substrate coupling in mixed-signal IC's

Proceedings of the conference on Design, automation and test in Europe - DATE '99, 1999

Accurate modeling of noise coupling effects due to crosstalk via the substrate is an increasingly... more Accurate modeling of noise coupling effects due to crosstalk via the substrate is an increasingly important concern for the design and verification of mixed analogdigital systems. In this paper we present a technique to accelerate the model computation using BEM methods that can be used for accurate and efficient extraction of substrate coupling parameters in mixed-signal designs.

Research paper thumbnail of Robust rational function approximation algorithm for model generation

Proceedings 1999 Design Automation Conference (Cat. No. 99CH36361)

The problem of computing rational function approximations to tabulated frequency data is of param... more The problem of computing rational function approximations to tabulated frequency data is of paramount importance in the modeling arena. In this paper we present a method for generating a state space model from tabular data in the frequency domain that solves some of the numerical difficulties associated with the traditional fitting techniques used in linear least squares approximations. An extension to the MIMO case is also derived.

Research paper thumbnail of Library compatible variational delay computation

IFIP International Federation for Information Processing, 2008

With technology steadily progressing into nanometer dimensions, precise control over all aspects ... more With technology steadily progressing into nanometer dimensions, precise control over all aspects of the fabrication process becomes an area of increasing concern. Process variations have immediate impact on circuit performance and behavior and standard design and signoff methodologies have to account for such variability. In this context, timing verification, already a challenging task due to the sheer complexity of todays designs, becomes an increasingly difficult problem. Statistical static timing analysis has been proposed as a solution to this problem, but most of the work has focused in the development of timing engines for computing delay propagation. Such tools rely on the availability of delay formulas accounting for both cell and interconnect delay that take into account unpredictable variability effects. In this paper, we concentrate on the impact of interconnect on delay and propose an extension to the standard modeling strategies that is variation-aware and compatible with such statistical engines. Our approach, based on a specific type of perturbation analysis, allows for the analytical computation of the quantities needed for statistical delay propagation. We also show how perturbation analysis can be performed when only the standard delay table lookup models are available for the standard cells. This makes the proposed approach compatible with existing timing analysis frameworks. Results from applying our proposed modeling strategy to computing delays and slews in several instances accurately match similar results obtained using electrical level simulation.

Research paper thumbnail of Efficient Representation and Analysis of Power Grids

2008 Design, Automation and Test in Europe, 2008

Modern deep sub-micron ULSI designs with hundreds of millions of devices require huge grids for p... more Modern deep sub-micron ULSI designs with hundreds of millions of devices require huge grids for power distribution. Such grids, operating with increasingly low-power voltages, are a design limiting factor and accurate analysis of their behavior is of paramount importance as any voltage drops can seriously impact performance or functionality. As power grid models have millions of unknowns, highly optimized special purpose simulation tools are required to handle the time and memory complexity of solving for their dynamic behavior. In this work, we propose a hierarchical matrix representation of the power grid model that is both space and time efficient. With this representation, reduced storage matrix factors are efficiently computed and applied in the analysis at every time-step of the simulation. Results show an almost linear complexity growth, namely O(nlog a (n)), for some small constant a, in both space and time, when using this matrix representation. Comparisons of our academic implementation with production-quality code proves this method to be very efficient when dealing with the simulation of large power grid models

Research paper thumbnail of Coupled Circuit-Interconnect Modeling and Simulation

VLSI: Integrated Systems on Silicon, 1997

In this paper we discuss generating low order models for efficient coupled circuitinterconnect si... more In this paper we discuss generating low order models for efficient coupled circuitinterconnect simulation. The ever increasing speeds and shrinking feature sizes that are typical of state of the art integrated circuits designs have made coupling due to interconnect and packaging a very important, sometimes dominant, factor in system performance. The ability to efficiently perform coupled circuit-interconnect simulation before fabrication is essential in order to detect signal degradation due to delays or crosstalk. We first discuss methods of generating models for both two and three dimensional interconnect and then present a general, guaranteed-stable, model order reduction technique to reduce the order of the interconnect models.

Research paper thumbnail of Order reduction techniques for coupled multi-domain electromagnetic based models

This work presents a comprehensive flow able to efficiently generate reduced order models for rea... more This work presents a comprehensive flow able to efficiently generate reduced order models for realistic, hierarchy aware, Electromagnetic (EM) based models. Knowledge of the structure of the problem is explicitly exploited using domain partitioning and novel electromagnetic connector modeling techniques to generate a hierarchically coupled representation. This enables the efficient use of structure preserving block model order reduction techniques to generate block-wise compressed models that satisfy overall requirements, and provide cheap evaluation and simulation accurate approximations of the complete EM behaviour.