The recently completed research project DEEP-ER has developed a variety of hardware and software technologies to improve the I/O capabilities of next generation high-performance computers, and to enable applications recovering from the larger hardware failure rates expected on these machines. The heterogeneous Cluster-Booster architecture --first introduced in the predecessor DEEP project-- has been extended by a multi-level memory hierarchy employing non-volatile and network-attached memory devices. Based on this hardware infrastructure, an I/O and resiliency software stack has been implemented combining and extending well established libraries and software tools, and sticking to standard user-interfaces. Real-world scientific codes have tested the projects' developments and demonstrated the improvements achieved without compromising the portability of the applications.

In this paper, we report on our recent efforts towards adapting a Discontinuous Galerkin Time-Domain solver for computational bioelectromagnetics to the novel, heterogeneous architecture proposed in the DEEP-ER european project on exascale computing. This architecture is based on the Cluster/Booster division concept which will be recalled. As a first step, we summarize the key features of the application and present the outcomes of a profiling of the code using the tools developed by DEEP-ER partners. We then go through the subsequent general improvements of the application as well as specific developments aimed at exploiting efficiently the DEEP-ER platform. This particularly includes porting the application to the Intel (R) Many Integrated Core Architecture. We conclude with an outlook on next steps, including the different Cluster/Booster division strategies.

This work proposes a Multiscale Hybrid-Mixed (MHM) method for the Maxwell equation in time domain. The MHM method is a consequence of a hybridization procedure, and emerges as a method that naturally incorporates multiple scales while provides solutions with high-order precision. The computation of local problems is embedded in the upscaling procedure, which are completely independent and thus may be naturally obtained using parallel computation facilities. In this talk, we present the new MHM method for the two-dimensional Maxwell equations in time domain (Transverse Magnetic mode). We address some theoretical aspects of the method and propose an extensive numerical validation. We conclude that the MHM method is naturally shaped to be used in parallel computing environments and appears to be a highly competitive option to handle realistic multiscale hyperbolic boundary value problems with precision on coarse meshes.

This paper is concerned with the development of a scalable high order finite element type solver for the numerical modeling of light interaction with nanometer scale structures. From the mathematical modeling point of view, one has to deal with the differential system of Maxwell equations in the time domain, coupled to an appropriate differential model of the behavior of the underlying material (which can be a dielectric and/or a metal) at optical frequencies. For the numerical solution of the resulting system of differential equations, we have designed a high order DGTD (Discontinuous Galerkin Time-Domain) solver that has been adapted to hybrid MIMD/SIMD computing. Here we discuss about this later aspect and report on preliminary performance results on the Curie system of the PRACE research infrastructure.

In this work, we are interested in the propagation of electromagnetic waves in complex media. More precisely, we would like to study time dependent wave propagation problems with strong multiscale features (possibly in space and time). In this context we would like to contribute in the design of innovative numerical methods particularly well suited to the simulation of such problems. Indeed when a PDE model is approximated via classical finite element type method, it may suffer from a loss of accuracy when the solution presents multiscale features on coarse meshes. To address this issue, we rely on the concept of multiscale basis functions that is one solution to allow for accuracy even on coarse meshes. These basis functions are defined via algebraic relations. Contrary to classical polynomial approximation, they render by themselves a part of the high-contrast features of the problem at hand. Recently, a new family of finite element methods has been introduced in [1]-[2], referred as Multiscale Hybrid-Mixed methods (MHM), which is well adapted to the simulation of high-contrast or heterogeneous problems. The underlying approach relies on a two level discretization. Shortly, basis functions computed on a fine (second level) mesh allow for the reconstruction of the solution on a coarse (first level) mesh. Such MHM have been initially designed in the context of stationary problems, such as Darcy flows. In this work, we propose to extend the concept of MHM to time dependent electromagnetic wave propagation problems. The model problem relies on the time dependent Maxwell's equations. The continuity of the electric field is relaxed via the introduction of a Lagrange multiplier. The solutions are expressed on a basis computed at the second level that incorporates the heterogeneity of the problem via the resolution of a PDE. Several schemes are proposed from implicit to explicit time schemes and continuous finite elements to discontinuous ones for the spatial discretization of the local problems at the second level.

During the last ten years, the discontinuous Galerkin time-domain (DGTD) method has progressively emerged as a viable alternative to well established finite-difference time-domain (FDTD) and finite-element time-domain (FETD) methods for the numerical simulation of electromagnetic wave propagation problems in the time-domain. We discuss here about the development and application of such a DTGD method for solving the system of time-domain Maxwell equations coupled to material models relevant to nanophotonics. Our efforts aim at improving the accuracy, flexibility and efficiency of the method in view of the numerical treatment of realistic problems.

The present work is about the development of a parallel non-conforming multi-element discontinuous Galerkin time-domain (DGTD) method for the simulation of the scattering of electromagnetic waves by metallic nanoparticles. Such nanoparticles most often have curvilinear shapes, therefore we propose a numerical modeling strategy which combines the use of an unstructured tetrahedral mesh for the discretization of the scattering structures with a structured (uniform cartesian) mesh for treating efficiently the rest of the domain. The overall goal is to increase the flexibility in the meshing process while decreasing the needs in computational resources for the target applications. The latter are here modeled by the system of 3D time-domain Maxwell equations coupled to a Drude dispersion model for taking into account the material properties of nanoparticles at optical frequencies. We propose an auxiliary differential equation (ADE) based DGTD method for solving the resulting system and present numerical results demonstrating the benefits of using non-conforming multi-element meshes in this particular application context.

We present a discontinuous finite element time-domain solver for the computer simulation of the interaction of light with nanometer scale structures. The method relies on a compact stencil high order interpolation of the electromagnetic field components within each cell of an unstructured tetrahedral mesh. This piecewise polynomial numerical approximation is allowed to be discontinuous from one mesh cell to another, and the consistency of the global approximation is obtained thanks to the definition of appropriate numerical traces of the fields on a face shared by two neighboring cells. Time integration is achieved using an explicit scheme and no global mass matrix inversion is required to advance the solution at each time step. Moreover, the resulting time-domain solver is particularly well adapted to parallel computing. In this paper, we discuss about recent contributions for improving the accuracy, flexibility and efficiency of the method, as well as its adaptation to physical models relevant to nanophotonic applications.

SUMMARYThe great majority of numerical calculations of electric energy deposition in human tissues exposed to microwaves are performed using the finite‐difference time‐domain (FDTD) method and voxel‐based geometrical models of the tissues. The straightforward implementation of the method and its computational efficiency are among the main reasons for FDTD being currently the leading method for numerical assessment of human exposure to electromagnetic waves. However, the rather difficult departure from the commonly used Cartesian grid and cell size limitations regarding the discretization of very detailed structures of human tissues are often recognized as the main weaknesses of the FDTD method in this application context. In particular, interfaces between tissues where sharp gradients of the electromagnetic field may occur are hardly modeled rigorously in these studies (this is generally referred as the staircasing effect). We present here an alternative numerical dosimetry methodology that is based on a DGTD method designed to work with non‐conforming cubic‐tetrahedral meshes for more flexibility in the discretization process of complex propagation scenes. For example, in the context of head tissues exposure to mobile phone radiation, the computation domain is divided in two regions: an unstructured tetrahedral mesh‐based heterogeneous model of head tissues and an orthogonal cartesian mesh of the vacuum part of the propagation domain. We present numerical results comparing this approach with strategies based on fully Cartesian and fully tetrahedral meshes of the whole computational domain. Copyright © 2013 John Wiley & Sons, Ltd.

The study of a multidomain coupling algorithm of numerical methods applied to direct acoustic waves simulation is the focus of this paper. The idea is to be able to use meshing techniques and numerical methods of different natures, depending on the domain area, in order to meet the local requirements of the computation. Here, the linearized Euler equations are solved by carrying out a coupling between a discontinuous Galerkin method running on an unstructured mesh and a finite difference method running on a Cartesian grid. The aim is to take into account complex geometries by running a discontinuous Galerkin method and run a finite difference method away from the obstacles to reduce computational costs. In this paper, two different discontinuous Galerkin/finite difference coupling algorithms are presented, and some associated validation results in terms of precision and stability are discussed. An application of a hybrid solver in the framework of an acoustic benchmark dedicated to complex geometries is also presented.

method (FDM), running on a Cartesian grid. The aim is to take into account complex geometries by running a DGM and run a FDM away from the obstacles to reduce computational cost. In this paper, we present a DG/FD coupling algorithm and discuss some preliminary validation elements.