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Louis J. Durlofsky - One of the best experts on this subject based on the ideXlab platform.

  • enhanced linearized reduced order models for subsurface flow simulation
    Journal of Computational Physics, 2011
    Co-Authors: Jincong He, J Saetrom, Louis J. Durlofsky
    Abstract:

    Trajectory piecewise linearization (TPWL) represents a promising approach for constructing reduced-order models. Using TPWL, new solutions are represented in terms of expansions around previously simulated (and saved) solutions. High degrees of efficiency are achieved when the representation is projected into a low-dimensional space using a Basis constructed by proper orthogonal decomposition of snapshots generated in a training run. In recent work, a TPWL procedure applicable for two-phase subsurface flow problems was presented. The method was shown to perform well for many cases, such as those with no density differences between phases, though accuracy and robustness were found to degrade in other cases. In this work, these limitations are shown to be related to model accuracy at key locations and model stability. Enhancements addressing both of these issues are introduced. A new TPWL procedure, referred to as local resolution TPWL, enables key grid blocks (such as those containing injection or production wells) to be represented at full resolution; i.e., these blocks are not projected into the low-dimensional space. This leads to high accuracy at selected locations, and will be shown to improve the accuracy of important simulation quantities such as injection and production rates. Next, two techniques for enhancing the stability of the TPWL model are presented. The first approach involves a Basis optimization procedure in which the number of columns in the Basis Matrix is determined to minimize the spectral radius of an appropriately defined amplification Matrix. The second procedure incorporates a Basis Matrix constructed using snapshots from a simulation with equal phase densities. Both approaches are compatible with the local resolution procedure. Results for a series of test cases demonstrate the accuracy and stability provided by the new treatments. Finally, the TPWL model is used as a surrogate in a direct search optimization algorithm, and comparison with results using the full-order model demonstrates the efficacy of the enhanced TPWL procedures for this application.

  • development and application of reduced order modeling procedures for subsurface flow simulation
    International Journal for Numerical Methods in Engineering, 2009
    Co-Authors: M A Cardoso, Louis J. Durlofsky, Pallav Sarma
    Abstract:

    The optimization of subsurface flow processes is important for many applications, including oil field operations and the geological storage of carbon dioxide. These optimizations are very demanding computationally due to the large number of flow simulations that must be performed and the typically large dimension of the simulation models. In this work, reduced-order modeling (ROM) techniques are applied to reduce the simulation time of complex large-scale subsurface flow models. The procedures all entail proper orthogonal decomposition (POD), in which a high-fidelity training simulation is run, solution snapshots are stored, and an eigen-decomposition (SVD) is performed on the resulting data Matrix. Additional recently developed ROM techniques are also implemented, including a snapshot clustering procedure and a missing point estimation technique to eliminate rows from the POD Basis Matrix. The implementation of the ROM procedures into a general-purpose research simulator is described. Extensive flow simulations involving water injection into a geologically complex 3D oil reservoir model containing 60 000 grid blocks are presented. The various ROM techniques are assessed in terms of their ability to reproduce high-fidelity simulation results for different well schedules and also in terms of the computational speedups they provide. The numerical solutions demonstrate that the ROM procedures can accurately reproduce the reference simulations and can provide speedups of up to an order of magnitude when compared with a high-fidelity model simulated using an optimized solver. Copyright © 2008 John Wiley & Sons, Ltd.

Pallav Sarma - One of the best experts on this subject based on the ideXlab platform.

  • development and application of reduced order modeling procedures for subsurface flow simulation
    International Journal for Numerical Methods in Engineering, 2009
    Co-Authors: M A Cardoso, Louis J. Durlofsky, Pallav Sarma
    Abstract:

    The optimization of subsurface flow processes is important for many applications, including oil field operations and the geological storage of carbon dioxide. These optimizations are very demanding computationally due to the large number of flow simulations that must be performed and the typically large dimension of the simulation models. In this work, reduced-order modeling (ROM) techniques are applied to reduce the simulation time of complex large-scale subsurface flow models. The procedures all entail proper orthogonal decomposition (POD), in which a high-fidelity training simulation is run, solution snapshots are stored, and an eigen-decomposition (SVD) is performed on the resulting data Matrix. Additional recently developed ROM techniques are also implemented, including a snapshot clustering procedure and a missing point estimation technique to eliminate rows from the POD Basis Matrix. The implementation of the ROM procedures into a general-purpose research simulator is described. Extensive flow simulations involving water injection into a geologically complex 3D oil reservoir model containing 60 000 grid blocks are presented. The various ROM techniques are assessed in terms of their ability to reproduce high-fidelity simulation results for different well schedules and also in terms of the computational speedups they provide. The numerical solutions demonstrate that the ROM procedures can accurately reproduce the reference simulations and can provide speedups of up to an order of magnitude when compared with a high-fidelity model simulated using an optimized solver. Copyright © 2008 John Wiley & Sons, Ltd.

H V Poor - One of the best experts on this subject based on the ideXlab platform.

  • measurement Matrix design for compressive sensing based mimo radar
    IEEE Transactions on Signal Processing, 2011
    Co-Authors: Yao Yu, Athina P Petropulu, H V Poor
    Abstract:

    In colocated multiple-input multiple-output (MIMO) radar using compressive sensing (CS), a receive node compresses its received signal via a linear transformation, referred to as a measurement Matrix. The samples are subsequently forwarded to a fusion center, where an l1-optimization problem is formulated and solved for target information. CS-based MIMO radar exploits target sparsity in the angle-Doppler-range space and thus achieves the high localization performance of traditional MIMO radar but with significantly fewer measurements. The measurement Matrix affects the recovery performance. A random Gaussian measurement Matrix, typically used in CS problems, does not necessarily result in the best possible detection performance for the Basis Matrix corresponding to the MIMO radar scenario. This paper considers optimal measurement Matrix design with the optimality criterion depending on the coherence of the sensing Matrix (CSM) and/or signal-to-interference ratio (SIR). Two approaches are proposed: the first one minimizes a linear combination of CSM and the inverse SIR, and the second one imposes a structure on the measurement Matrix and determines the parameters involved so that the SIR is enhanced. Depending on the transmit waveforms, the second approach can significantly improve the SIR, while maintaining a CSM comparable to that of the Gaussian random measurement Matrix (GRMM). Simulations indicate that the proposed measurement matrices can improve detection accuracy as compared to a GRMM.

  • mimo radar using compressive sampling
    IEEE Journal of Selected Topics in Signal Processing, 2010
    Co-Authors: Yao Yu, Athina P Petropulu, H V Poor
    Abstract:

    A multiple-input multiple-output (MIMO) radar system is proposed for obtaining angle and Doppler information on potential targets. Transmitters and receivers are nodes of a small scale wireless network and are assumed to be randomly scattered on a disk. The transmit nodes transmit uncorrelated waveforms. Each receive node applies compressive sampling to the received signal to obtain a small number of samples, which the node subsequently forwards to a fusion center. Assuming that the targets are sparsely located in the angle-Doppler space, based on the samples forwarded by the receive nodes the fusion center formulates an l 1 -optimization problem, the solution of which yields target angle and Doppler information. The proposed approach achieves the superior resolution of MIMO radar with far fewer samples than required by other approaches. This implies power savings during the communication phase between the receive nodes and the fusion center. Performance in the presence of a jammer is analyzed for the case of slowly moving targets. Issues related to forming the Basis Matrix that spans the angle-Doppler space, and for selecting a grid for that space are discussed. Extensive simulation results are provided to demonstrate the performance of the proposed approach at difference jammer and noise levels.

M A Cardoso - One of the best experts on this subject based on the ideXlab platform.

  • development and application of reduced order modeling procedures for subsurface flow simulation
    International Journal for Numerical Methods in Engineering, 2009
    Co-Authors: M A Cardoso, Louis J. Durlofsky, Pallav Sarma
    Abstract:

    The optimization of subsurface flow processes is important for many applications, including oil field operations and the geological storage of carbon dioxide. These optimizations are very demanding computationally due to the large number of flow simulations that must be performed and the typically large dimension of the simulation models. In this work, reduced-order modeling (ROM) techniques are applied to reduce the simulation time of complex large-scale subsurface flow models. The procedures all entail proper orthogonal decomposition (POD), in which a high-fidelity training simulation is run, solution snapshots are stored, and an eigen-decomposition (SVD) is performed on the resulting data Matrix. Additional recently developed ROM techniques are also implemented, including a snapshot clustering procedure and a missing point estimation technique to eliminate rows from the POD Basis Matrix. The implementation of the ROM procedures into a general-purpose research simulator is described. Extensive flow simulations involving water injection into a geologically complex 3D oil reservoir model containing 60 000 grid blocks are presented. The various ROM techniques are assessed in terms of their ability to reproduce high-fidelity simulation results for different well schedules and also in terms of the computational speedups they provide. The numerical solutions demonstrate that the ROM procedures can accurately reproduce the reference simulations and can provide speedups of up to an order of magnitude when compared with a high-fidelity model simulated using an optimized solver. Copyright © 2008 John Wiley & Sons, Ltd.

Yao Yu - One of the best experts on this subject based on the ideXlab platform.

  • measurement Matrix design for compressive sensing based mimo radar
    IEEE Transactions on Signal Processing, 2011
    Co-Authors: Yao Yu, Athina P Petropulu, H V Poor
    Abstract:

    In colocated multiple-input multiple-output (MIMO) radar using compressive sensing (CS), a receive node compresses its received signal via a linear transformation, referred to as a measurement Matrix. The samples are subsequently forwarded to a fusion center, where an l1-optimization problem is formulated and solved for target information. CS-based MIMO radar exploits target sparsity in the angle-Doppler-range space and thus achieves the high localization performance of traditional MIMO radar but with significantly fewer measurements. The measurement Matrix affects the recovery performance. A random Gaussian measurement Matrix, typically used in CS problems, does not necessarily result in the best possible detection performance for the Basis Matrix corresponding to the MIMO radar scenario. This paper considers optimal measurement Matrix design with the optimality criterion depending on the coherence of the sensing Matrix (CSM) and/or signal-to-interference ratio (SIR). Two approaches are proposed: the first one minimizes a linear combination of CSM and the inverse SIR, and the second one imposes a structure on the measurement Matrix and determines the parameters involved so that the SIR is enhanced. Depending on the transmit waveforms, the second approach can significantly improve the SIR, while maintaining a CSM comparable to that of the Gaussian random measurement Matrix (GRMM). Simulations indicate that the proposed measurement matrices can improve detection accuracy as compared to a GRMM.

  • mimo radar using compressive sampling
    IEEE Journal of Selected Topics in Signal Processing, 2010
    Co-Authors: Yao Yu, Athina P Petropulu, H V Poor
    Abstract:

    A multiple-input multiple-output (MIMO) radar system is proposed for obtaining angle and Doppler information on potential targets. Transmitters and receivers are nodes of a small scale wireless network and are assumed to be randomly scattered on a disk. The transmit nodes transmit uncorrelated waveforms. Each receive node applies compressive sampling to the received signal to obtain a small number of samples, which the node subsequently forwards to a fusion center. Assuming that the targets are sparsely located in the angle-Doppler space, based on the samples forwarded by the receive nodes the fusion center formulates an l 1 -optimization problem, the solution of which yields target angle and Doppler information. The proposed approach achieves the superior resolution of MIMO radar with far fewer samples than required by other approaches. This implies power savings during the communication phase between the receive nodes and the fusion center. Performance in the presence of a jammer is analyzed for the case of slowly moving targets. Issues related to forming the Basis Matrix that spans the angle-Doppler space, and for selecting a grid for that space are discussed. Extensive simulation results are provided to demonstrate the performance of the proposed approach at difference jammer and noise levels.