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Practical applications of controlled-source electromagnetic (EM) modelling require solutions for multiple sources at several frequencies, thus leading to a dramatic increase of the computational cost. In this paper, we present an approach using block Krylov subspace solvers that are iterative methods especially designed for problems with multiple right-hand sides (RHS). Their main advantage is the shared subspace for approximate solutions, hence, these methods are expected to converge in less iterations than the corresponding standard solver applied to each linear system. Block solvers also share the same preconditioner, which is constructed only once. Simultaneously computed block operations have better utilization of cache due to the less frequent access to the system matrix. In this paper, we implement two different block solvers for sparse matrices resulting from the finite-difference and the finite-element discretizations, discuss the computational cost of the algorithms and study their dependence on the number of RHS given at once. The effectiveness of the proposed methods is demonstrated on two EMsurvey scenarios, including a large marine model. As the results of the simulations show, when a powerful preconditioning is employed, block methods are faster than standard iterative techniques in terms of both iterations and time. [ABSTRACT FROM AUTHOR]

We present the capabilities and results of the Parallel Edge-based Tool for Geophysical Electromagnetic modeling (PETGEM), as well as the physical and numerical foundations upon which it has been developed. PETGEM is an open-source and distributed parallel Python code for fast and highly accurate modeling of 3D marine controlled-source electromagnetic (3D CSEM) problems. We employ the Nédélec Edge Finite Element Method (EFEM) which offers a good trade-off between accuracy and number of degrees of freedom, while naturally supporting unstructured tetrahedral meshes. We have particularised this new modeling tool to the 3D CSEM problem for infinitesimal point dipoles asumming arbitrarily isotropic media for low-frequencies approximations. In order to avoid source-singularities, PETGEM solves the frequency-domain Maxwell's equations of the secondary electric field, and the primary electric field is calculated analytically for homogeneous background media. We assess the PETGEM accuracy using classical tests with known analytical solutions as well as recent published data of real life geological scenarios. This assessment proves that this new modeling tool reproduces expected accurate solutions in the former tests, and its flexibility on realistic 3D electromagnetic problems. Furthermore, an automatic mesh adaptation strategy for a given frequency and specific source position is presented. We also include a scalability study based on fundamental metrics for high-performance computing (HPC) architectures. [ABSTRACT FROM AUTHOR]

We introduce a new synthetic marine model for 3D controlled-source electromagnetic method (CSEM) surveys. The proposed model includes relevant features for the electromagnetic geophysical community such as large conductivity contrast with vertical transverse isotropy and a complex bathymetry profile. In this paper, we present the experimental setup and several 3D CSEM simulations in the presence of a resistivity unit denoting a hydrocarbon reservoir. We employ a parallel and high-order vector finite element routine to perform the CSEM simulations. By using tailored meshes, several scenarios are simulated to assess the influence of the reservoir unit presence on the electromagnetic responses. Our numerical assessment confirms that resistivity unit strongly influences the amplitude and phase of the electromagnetic measurements. We investigate the code performance for the solution of fundamental frequencies on high-performance computing architectures. Here, excellent performance ratios are obtained. Our benchmark model and its modeling results are developed under an open-source scheme that promotes easy access to data and reproducible solutions. [ABSTRACT FROM AUTHOR]

We present a parallel and high-order Nédélec finite element solution for the marine controlled-source electromagnetic (CSEM) forward problem in 3-D media with isotropic conductivity. Our parallel Python code is implemented on unstructured tetrahedral meshes, which support multiple-scale structures and bathymetry for general marine 3-D CSEM modelling applications. Based on a primary/secondary field approach, we solve the diffusive form of Maxwell's equations in the low-frequency domain. We investigate the accuracy and performance advantages of our new high-order algorithm against a low-order implementation proposed in our previous work. The numerical precision of our high-order method has been successfully verified by comparisons against previously published results that are relevant in terms of scale and geological properties. A convergence study confirms that high-order polynomials offer a better trade-off between accuracy and computation time. However, the optimum choice of the polynomial order depends on both the input model and the required accuracy as revealed by our tests. Also, we extend our adaptive-meshing strategy to high-order tetrahedral elements. Using adapted meshes to both physical parameters and high-order schemes, we are able to achieve a significant reduction in computational cost without sacrificing accuracy in the modelling. Furthermore, we demonstrate the excellent performance and quasi-linear scaling of our implementation in a state-of-the-art high-performance computing architecture. [ABSTRACT FROM AUTHOR]

The performance and scalability of atmospheric transport models on high performance computing environments is often far from optimal for multiple reasons including, for example, sequential input and output, synchronous communications, work unbalance, memory access latency or lack of task overlapping. We investigate how different software optimizations and porting to non general-purpose hardware architectures improve code scalability and execution times considering, as an example, the FALL3D volcanic ash transport model. To this purpose, we implement the FALL3D model equations in the WARIS framework, a software designed from scratch to solve in a parallel and efficient way different geoscience problems on a wide variety of architectures. In addition, we consider further improvements in WARIS such as hybrid MPI-OMP parallelization, spatial blocking, auto-tuning and thread affinity. Considering all these aspects together, the FALL3D execution times for a realistic test case running on general-purpose cluster architectures (Intel Sandy Bridge) decrease by a factor between 7 and 40 depending on the grid resolution. Finally, we port the application to Intel Xeon Phi (MIC) and NVIDIA GPUs (CUDA) accelerator-based architectures and compare performance, cost and power consumption on all the architectures. Implications on time-constrained operational model configurations are discussed. [ABSTRACT FROM AUTHOR]

We present an elaborate preconditioning scheme for Krylov subspace methods which has been developed to improve the performance and reduce the execution time of parallel node-based finite-element (FE) solvers for 3-D electromagnetic (EM) numerical modelling in exploration geophysics. This new preconditioner is based on algebraic multigrid (AMG) that uses different basic relaxation methods, such as Jacobi, symmetric successive over-relaxation (SSOR) and Gauss–Seidel, as smoothers and the wave front algorithm to create groups, which are used for a coarse-level generation. We have implemented and tested this new preconditioner within our parallel nodal FE solver for 3-D forward problems in EM induction geophysics. We have performed series of experiments for several models with different conductivity structures and characteristics to test the performance of our AMG preconditioning technique when combined with biconjugate gradient stabilized method. The results have shown that, the more challenging the problem is in terms of conductivity contrasts, ratio between the sizes of grid elements and/or frequency, the more benefit is obtained by using this preconditioner. Compared to other preconditioning schemes, such as diagonal, SSOR and truncated approximate inverse, the AMG preconditioner greatly improves the convergence of the iterative solver for all tested models. Also, when it comes to cases in which other preconditioners succeed to converge to a desired precision, AMG is able to considerably reduce the total execution time of the forward-problem code—up to an order of magnitude. Furthermore, the tests have confirmed that our AMG scheme ensures grid-independent rate of convergence, as well as improvement in convergence regardless of how big local mesh refinements are. In addition, AMG is designed to be a black-box preconditioner, which makes it easy to use and combine with different iterative methods. Finally, it has proved to be very practical and efficient in the parallel context. [ABSTRACT FROM PUBLISHER]

We present a nodal finite-element method that can be used to compute in parallel highly accurate solutions for 3-D controlled-source electromagnetic forward-modelling problems in anisotropic media. Secondary coupled-potential formulation of Maxwell's equations allows to avoid the singularities introduced by the sources, while completely unstructured tetrahedral meshes and mesh refinement support an accurate representation of geological and bathymetric complexity and improve the solution accuracy. Different complex iterative solvers and an efficient pre-conditioner based on the sparse approximate inverse are used for solving the resulting large sparse linear system of equations. Results are compared with the ones of other researchers to check the accuracy of the method. We demonstrate the performance of the code in large problems with tens and even hundreds of millions of degrees of freedom. Scalability tests on massively parallel computers show that our code is highly scalable. [ABSTRACT FROM AUTHOR]

Reverse-Time Migration (RTM) is a state-of-the-art technique in seismic acoustic imaging, because of the quality and integrity of the images it provides. Oil and gas companies trust RTM with crucial decisions on multi-million-dollar drilling investments. But RTM requires vastly more computational power than its predecessor techniques, and this has somewhat hindered its practical success. On the other hand, despite multi-core architectures promise to deliver unprecedented computational power, little attention has been devoted to mapping efficiently RTM to multi-cores. In this paper, we present a mapping of the RTM computational kernel to the IBM Cell/B.E. processor that reaches close-to-optimal performance. The kernel proves to be memory-bound and it achieves a 98% utilization of the peak memory bandwidth. Our Cell/B.E. implementation outperforms a traditional processor (PowerPC 970MP) in terms of performance (with an 15.0× speedup) and energy-efficiency (with a 10.0× increase in the GFlops/W delivered). Also, it is the fastest RTM implementation available to the best of our knowledge. These results increase the practical usability of RTM. Also, the RTM-Cell/B.E. combination proves to be a strong competitor in the seismic arena. [ABSTRACT FROM AUTHOR]