HOMAR Associate Team

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# To implement the proposed MHM-DGTD solution strategy on modern parallel computing architectures combining coarse grain (MIMD - Multiple Instruction Multiple Data) and fine grian (SIMD - Single Instruction Multiple Data) processing units;

# To design and analyse new MHM methods for the system of time-domain elastodynamic equations for modeling elastic wave propagation in anisotropic media;

Finite element methods are frequently adopted to approximate the solution of such PDE  models. Nevetheless, it is well-known that the accuracy of numerical solutions may seriously deteriorate on coarse meshes when they show multiscale or high-contrast features. Such an issue has led to the concept of multiscale basis functions in the seminal work [Babuska and Osborn, 1983] (further extended to the two-dimensional case in [Hou and Wu, 1997]) and allowed numerical methods to be precise on coarse meshes. Such physically rooted basis functions are the counterpart of polynomial basis functions generally adopted in classical finite element schemes, which are defined on a purely algebraic setting. Recently, researchers at LNCC introduced a family of finite element methods particularly adapted to be used in high-contrast or heterogeneous coefficients problems, [Araya et al., 2013]-[Harder et al., 2013], named Multiscale Hybrid-Mixed (MHM) methods. These novel finite element methods share the following properties: (i) Stable and high-order convergent; (ii) Accurate on coarse meshes; (iii) Naturally adapted to high-performance parallel computing; (iv) Induce a face-based a posteriori error estimator (to drive mesh adaptivity); (v) Locally conservative.

HOMAR is funded by Inria's Direction of the European and International Partnerships Department and by FAPERJ (Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro)

[[Partnership  | Partners and participants]]
[[Meetings    | Meetings]]
[[Publications | Publications]]
[[HOMAR/Results | Results]]

[[Results     | Results]]

[[Partnership | Partners and participants]]

* [[Partnership | Partners and participants]]
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!! Partners and participants

(:linebreaks:)

!! Inria Sophia Antipolis - Méditerranée, %newwin% [[http://www-sop.inria.fr/nachos | Nachos project-team]]
* %newwin% [[http://www-sop.inria.fr/nachos/index.php/People/S-Lanteri | Stéphane Lanteri]]
* %newwin% [[http://www-sop.inria.fr/nachos/index.php/People/M-Lallemand | Marie Hélène Lallemand]]
* %newwin% [[http://www-sop.inria.fr/nachos/index.php/People/R-Leger | Raphaël Léger]]
* %newwin% [[http://www-sop.inria.fr/nachos/index.php/People/C-Scheid | Claire Scheid]]

!! %newwin% [[http://www.lncc.br | LNCC]], Petrópolis, Brazil
* %newwin% [[http://www.lncc.br/~atagomes | Antônio Tadeu Azevedo Gomes]]
* %newwin% [[http://www.lncc.br/~alm | Alexandre Madureira]]
* %newwin% [[http://www.lncc.br/~valentin | Frédéric Valentin]]

!! Universidad Católica de Valparaiso, Chile
* %newwin% [[http://dparedesfem.wix.com/home | Diego Paredes]]

The main scientific goals of this collaboration iare:

The main scientific goals of HOMAR  are:

!! [+High performance Multiscale Algorithms for wave pRopagation problems+]

!! High performance Multiscale Algorithms for wave pRopagation problems

! Inria Sophia Antipolis - Méditerranée, %newwin% [[http://www-sop.inria.fr/nachos | Nachos project-team]]

! %newwin% [[http://www.lncc.br | LNCC]], Petrópolis, Brazil

! Universidad Católica de Valparaiso, Chile

!!! Scientific context

!!! Partners and participants

!!! Inria Sophia Antipolis - Méditerranée, %newwin% [[http://www-sop.inria.fr/nachos | Nachos project-team]]

!!! %newwin% [[http://www.lncc.br | LNCC]], Petrópolis, Brazil

!!! Universidad Católica de Valparaiso, Chile

!!! LNCC, Petrópolis, Brazil
* [[http://www.lncc.br/~atagomes | Antônio Tadeu Azevedo Gomes]]
* [[http://www.lncc.br/~alm | Alexandre Madureira]]
* [[http://www.lncc.br/~valentin | Frédéric Valentin]]

* [[http://dparedesfem.wix.com/home | Diego Paredes]]

!!! Inria Sophia Antipolis - Méditerranée, %newwin% [[http://www-sop.inria.fr/nachos | Nachos project-team]]\\\

!!! LNCC, Petrópolis, Brazil\\\

!!! Universidad Católica de Valparaiso, Chile\\\

!!! Inria Sophia Antipolis - Méditerranée, %newwin% [[http://www-sop.inria.fr/nachos | Nachos project-team]]

!!! LNCC, Petrópolis, Brazil
* [[http://www.lncc.br/~atagomes | Antônio Tadeu Azevedo Gomes]],

Finite element methods are frequently adopted to approximate the solution of such PDE  models. Nevetheless, it is well-known that the accuracy of numerical solutions may seriously deteriorate on coarse meshes when they show multiscale or high-contrast features. Such an issue has led to the concept of multiscale basis functions in the seminal work [Babuska and Osborn, 1983] (further extended to the two-dimensional case in [Hou and Wu, 1997]) and allowed numerical methods to be precise on coarse meshes. Such physically rooted basis functions are the counterpart of polynomial basis functions generally adopted in classical finite element schemes, which are defined on a purely algebraic setting. Recently, researchers at LNCC introduced a family of finite element methods particularly adapted to be used in high-contrast or heterogeneous coefficients problems, [Araya et al., 2013]- [Harder et al., 2013], named Multiscale Hybrid-Mixed (MHM) methods. These novel finite element methods share the following properties: (i) Stable and high-order convergent; (ii) Accurate on coarse meshes; (iii) Naturally adapted to high-performance parallel computing; (iv) Induce a face-based a posteriori error estimator (to drive mesh adaptivity); (v) Locally conservative.

@@ %black% Inria Sophia Antipolis - Méditerranée, %newwin% [[http://www-sop.inria.fr/nachos | Nachos project-team]]@@

@@Inria Sophia Antipolis - Méditerranée, %newwin% [[http://www-sop.inria.fr/nachos | Nachos project-team]]@@

'''Inria Sophia Antipolis - Méditerranée, Nachos project-team'''

!!! Partner and participants

Inria Sophia Antipolis - Méditerranée, Nachos project-team

* %newwin% [[http://www-sop.inria.fr/nachos/index.php/Main/StephaneLanteri | Stéphane Lanteri]]
* Marie Hélène Lallemand
* Raphaël Léger
* %newwin% [[http://math.unice.fr/~cscheid | Claire Scheid]]

* %newwin% [[http://www-sop.inria.fr/nachos/index.php/Main/St%E9phaneLanteri | Stéphane Lanteri]]

!!! Partnership

! High performance Multiscale Algorithms for wave pRopagation problems

!! High performance Multiscale Algorithms for wave pRopagation problems

>>

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Finite element methods are frequently adopted to approximate the solution of such PDE  models. Nevetheless, it is well-known that the accuracy of numerical solutions may seriously deteriorate on coarse meshes when they show multiscale or high-contrast features. Such an issue has led to the concept of multiscale basis functions in the seminal work [Babuska and Osborn, 1983] (further extended to the two-dimensional case in [Hou and Wu, 1997]) and allowed numerical methods to be precise on coarse meshes. Such physically rooted basis functions are the counterpart of polynomial basis functions generally adopted in classical finite element schemes, which are defined on a purely algebraic setting. Recently, researchers at LNCC introduced a family of finite element methods particularly adapted to be used in high-contrast or heterogeneous coefficients problems, [Araya et al., 2013]- [Harder et al., 2013], named Multiscale Hybrid-Mixed (MHM) methods. These novel finite element methods share the following properties: (i) Stable and high-order convergent; (ii) Accurate on coarse meshes; (iii) Naturally adapted to high-performance parallel computing; (iv) Induce a face-based a posteriori error estimator (to drive mesh adaptivity); (v) Locally conservative.

Finite element methods are frequently adopted to approximate the solution of such PDE  models. Nevetheless, it is well-known that the accuracy of numerical solutions may seriously deteriorate on coarse meshes when they show multiscale or high-contrast features. Such an issue has led to the concept of multiscale basis functions in the seminal work [Babuska and Osborn, 1983] (further extended to the two-dimensional case in [Hou and Wu, 1997]) and allowed numerical methods to be precise on coarse meshes. Such physically rooted basis functions are the counterpart of polynomial basis functions generally adopted in classical finite element schemes, which are defined on a purely algebraic setting. Recently, researchers at LNCC introduced a family of finite element methods particularly adapted to be used in high-contrast or heterogeneous coefficients problems, [Araya et al., 2013]- [Harder et al., 2013], named Multiscale Hybrid-Mixed (MHM) methods. These novel finite element methods share the following properties: (i) Stable and high-order convergent; (ii) Accurate on coarse meshes; (iii) Naturally adapted to high-performance parallel computing; (iv) Induce a face-based a posteriori error estimator (to drive mesh adaptativity); (v) Locally conservative.

The general scientific context of this collaboration is the study of time dependent wave propagation problems with strong multiscale features (in space and time). The general goal is the design, analysis and implementation of a family of innovative high performance numerical methods particularly well suited to the simulation of multiscale wave propagation problems. Mathematical models based on partial differential equations (PDE) embedding multiscale features occur in a wide range of scientific and technological applications involving wave propagation in heterogeneous media.

The general scientific context of this collaboration is the study of time dependent wave propagation problems with strong multiscale features (in space and time). The general goal is the design, analysis and implementation of a family of innovative high performance numerical meth- ods particularly well suited to the simulation of multiscale wave propagation problems. Math- ematical models based on partial differential equations (PDE) embedding multiscale features occur in a wide range of scientific and technological applications involving wave propagation in heterogenous media.

High performance Multiscale Algorithms for wave pRopagation problems

(:title HOMAR Associate Team:)