http://www-sop.inria.fr/nachos/pics/homar/1st_level_mesh.png %width=250px% http://www-sop.inria.fr/nachos/pics/homar/2nd_level_mesh.png

http://www-sop.inria.fr/nachos/pics/homar/1st_level_mesh.png %width=200px% http://www-sop.inria.fr/nachos/pics/homar/2nd_level_mesh.png

http://www-sop.inria.fr/nachos/pics/homar/ten_quad4edge_balls-eps-converted-to.png %width=200px% http://www-sop.inria.fr/nachos/pics/homar/mhm_4_16_16_mesh.png

http://www-sop.inria.fr/nachos/pics/homar/ten_quad4edge_balls-eps-converted-to.png %width=260px% http://www-sop.inria.fr/nachos/pics/homar/mhm_4_16_16_mesh.png

http://www-sop.inria.fr/nachos/pics/homar/ten_quad5edge_balls-eps-converted-to.png %width=260px% http://www-sop.inria.fr/nachos/pics/homar/mhm_4_16_16_mesh.png

http://www-sop.inria.fr/nachos/pics/homar/ten_quad5edge_balls-eps-converted-to.png

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

1. To design and analyze 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. Nevertheless, 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).

(:linebreaks:)

Partners and participants Meetings Publications Results

Results

Partners and participants Meetings Publications Results

Partners and participants

The main scientific goals of this collaboration are:

The main scientific goals of this collaboration iare:

High performance Multiscale Algorithms for wave pRopagation problems

High performance Multiscale Algorithms for wave pRopagation problems

Inria Sophia Antipolis - Méditerranée, Nachos project-team

LNCC, Petrópolis, Brazil

Universidad Católica de Valparaiso, Chile

Scientific context

Partners and participants

Inria Sophia Antipolis - Méditerranée, Nachos project-team

LNCC, Petrópolis, Brazil

Universidad Católica de Valparaiso, Chile

LNCC, Petrópolis, Brazil

• Antônio Tadeu Azevedo Gomes
• Alexandre Madureira
• Frédéric Valentin

• Diego Paredes

Inria Sophia Antipolis - Méditerranée, Nachos project-team

LNCC, Petrópolis, Brazil

Universidad Católica de Valparaiso, Chile

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

LNCC, Petrópolis, Brazil

* Antônio Tadeu Azevedo Gomes

Universidad Católica de Valparaiso, Chile

* Diego Paredes

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.

Inria Sophia Antipolis - Méditerranée, Nachos project-team

LNCC, Petrópolis, Brazil

• Antônio Tadeu Azevedo Gomes,
• Alexandre Madureira
• Frédéric Valentin

Inria Sophia Antipolis - Méditerranée, Nachos project-team

Inria Sophia Antipolis - Méditerranée, Nachos project-team

Partners and participants

Inria Sophia Antipolis - Méditerranée, Nachos project-team

• Stéphane Lanteri
• Marie Hélène Lallemand
• Raphaël Léger
• Claire Scheid

• Stéphane Lanteri

Partner and participants

Inria Sophia Antipolis - Méditerranée, Nachos project-team

• Stéphane Lanteri
• Marie Hélène Lallemand
• Raphaël Léger
• Claire Scheid

High performance Multiscale Algorithms for wave pRopagation problems

High performance Multiscale Algorithms for wave pRopagation problems

(:linebreaks:)

>>

Scientific context

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 adaptivity); (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.

(:linebreaks:)

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.

(:linebreaks:)

High performance Multiscale Algorithms for wave pRopagation problems

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.

(:title HOMAR Associate Team:)

High performance Multiscale Algorithms for wave pRopagation problems

(:title HOMAR Associate Team:)