Publications related to Tensor product

Riemannian Optimization For High-Dimensional Tensor Completion

Tensor completion aims to reconstruct a high-dimensional data set where the vast majority of entries is missing. The assumption of low-rank structure in the underlying original data allows us to cast the completion problem into an optimization problem rest ...

Siam Publications2016

MATHICSE Technical Report : Effective models for the multidimensional wave equation in heterogeneous media over long time and numerical homogenization

Timothée Noé Pouchon, Assyr Abdulle

A family of effective equations that capture the long time dispersive effects of wave propagation in heterogeneous media in an arbitrary large periodic spatial domain

\Omega \subset \mathbb{R}^d

over long time is proposed and analyzed. For a wave equatio ...

MATHICSE2016

Maxwell’s equations as a special case of deformation of a solid lattice in Euler’s coordinates

It is shown that the set of equations known as “Maxwell’s equations” perfectly describe two very different systems: (1) the usual electromagnetic phenomena in vacuum or in the matter and (2) the deformation of isotropic solid lattices, containing topologic ...

2016

Maxwell’s equations as a special case of deformation of a solid lattice in Euler’s coordinates

Gérard Gremaud

It is shown that the set of equations known as “Maxwell’s equations” perfectly describe two very different systems: (1) the usual electromagnetic phenomena in vacuum or in the matter and (2) the deformation of isotropic solid lattices, containing topologic ...

2016

Effective models for the multidimensional wave equation in heterogeneous media over long time and numerical homogenization

Timothée Noé Pouchon, Assyr Abdulle

A family of effective equations that capture the long time dispersive effects of wave propagation in heterogeneous media in an arbitrary large periodic spatial domain Omega subset of R-d is proposed and analyzed. For a wave equation with highly oscillatory ...

World Scientific Publ Co Pte Ltd2016

A 16-Channel 1.1mm2 Implantable Seizure Control SoC with Sub-μW/Channel Consumption and Closed-Loop Stimulation in 0.18μm CMOS

Alexandre Schmid, Mahsa Shoaran, Yusuf Leblebici, Amirhossein Shahshahani, Masoud Shahshahani

We present a 16-channel seizure detection system-on-chip (SoC) with 0.92μW/channel power dissipation in a total area of 1.1mm² including a closed-loop neural stimulator. A set of four features are extracted from the spatially filtered neural data to achiev ...

IEEE2016

MATHICSE Technical Report : Preconditioned low-rank Riemannian optimization for linear systems with tensor product structure

Daniel Kressner, Michael Maximilian Steinlechner

The numerical solution of partial differential equations on high-dimensional domains gives rise to computationally challenging linear systems. When using standard discretization techniques, the size of the linear system grows exponentially with the number ...

MATHICSE2015

Low-rank tensor approximation for high-order correlation functions of Gaussian random fields

Fabio Nobile, Daniel Kressner, Christine Tobler, Rajesh Kumar

Gaussian random fields are widely used as building blocks for modeling stochastic processes. This paper is concerned with the efficient representation of d-point correlations for such fields, which in turn enables the representation of more general stochas ...

2015

Efficient matrix computation for tensor-product isogeometric analysis: the use of sum factorization

Annalisa Buffa, Pablo Antolin Sanchez, Maurizio Martinelli

In this paper we discuss the use of the sum-factorization for the calculation of the integrals arising in Galerkin isogeometric analysis. While introducing very little change in an isogeometric code based on element-by-element quadrature and assembling, th ...

2015

Insight into the eigenmodes of plasmonic nanoclusters based on the Green's tensor method

Olivier Martin, Shourya Dutta Gupta

Assemblies of plasmonic nanoparticles possess exotic properties that are used in numerous applications. Their efficiency for specific applications strongly depends on the modes supported by the structure. In this paper, we extend the Green's tensor formali ...

Optical Soc Amer2015

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Riemannian Optimization For High-Dimensional Tensor Completion

MATHICSE Technical Report : Effective models for the multidimensional wave equation in heterogeneous media over long time and numerical homogenization

Maxwell’s equations as a special case of deformation of a solid lattice in Euler’s coordinates

Maxwell’s equations as a special case of deformation of a solid lattice in Euler’s coordinates

Effective models for the multidimensional wave equation in heterogeneous media over long time and numerical homogenization

A 16-Channel 1.1mm2 Implantable Seizure Control SoC with Sub-μW/Channel Consumption and Closed-Loop Stimulation in 0.18μm CMOS

MATHICSE Technical Report : Preconditioned low-rank Riemannian optimization for linear systems with tensor product structure

Low-rank tensor approximation for high-order correlation functions of Gaussian random fields

Efficient matrix computation for tensor-product isogeometric analysis: the use of sum factorization

Insight into the eigenmodes of plasmonic nanoclusters based on the Green's tensor method

MATHICSE Technical Report : Effective models for the multidimensional wave equation in heterogeneous media over long time and numerical homogenization

Maxwell’s equations as a special case of deformation of a solid lattice in Euler’s coordinates

Riemannian Optimization For High-Dimensional Tensor Completion

Maxwell’s equations as a special case of deformation of a solid lattice in Euler’s coordinates

Effective models for the multidimensional wave equation in heterogeneous media over long time and numerical homogenization

A 16-Channel 1.1mm2 Implantable Seizure Control SoC with Sub-μW/Channel Consumption and Closed-Loop Stimulation in 0.18μm CMOS

MATHICSE Technical Report : Preconditioned low-rank Riemannian optimization for linear systems with tensor product structure

Efficient matrix computation for tensor-product isogeometric analysis: the use of sum factorization

Insight into the eigenmodes of plasmonic nanoclusters based on the Green's tensor method

Low-rank tensor approximation for high-order correlation functions of Gaussian random fields