Parallel Processing For Gravity Inversion

Proceedings of: Second International Workshop on Sustainable Ultrascale Computing Systems (NESUS 2015). Krakow (Poland), September 10-11, 2015.In this paper results of recent updates of a simple algorithm for the inversion of gravity anomalies for 3D geosections in parallel computer systems are presented. A relaxation iterative principle was used updating step by step the geosection distribution of mass density. Selection of updates was done on basis of least squares error match of the update effect with the observed anomaly. Locally weighted least squares combined with the linear trend were used to obtain good inversion results for two-body geosections

Tem_357 Harnessing the Power of Digital Transformation, Artificial Intelligence and Big Data Analytics with Parallel Computing

Traditionally, 2D and especially 3D forward modeling and inversion of large geophysical datasets are performed on supercomputing clusters. This was due to the fact computing time taken by using PC was too time consuming. With the introduction of parallel computing, attempts have been made to perform computationally intensive tasks on PC or clusters of personal computers where the computing power was based on Central Processing Unit (CPU). It is further enhanced with Graphical Processing Unit (GPU) as the GPU has become affordable with the launch of GPU based computing devices. Therefore this paper presents a didactic concept in learning and applying parallel computing with the use of General Purpose Graphical Processing Unit (GPGPU) was carried out and perform preliminary testing in migrating existing sequential codes for solving initially 2D forward modeling of geophysical dataset. There are many challenges in performing these tasks mainly due to lack of some necessary development software tools, but the preliminary findings are promising. Traditionally, 2D and especially 3D forward modeling and inversion of large geophysical datasets are performed on supercomputing clusters. This was due to the fact computing time taken by using PC was too time consuming. With the introduction of parallel computing, attempts have been made to perform computationally intensive tasks on PC or clusters of personal computers where the computing power was based on Central Processing Unit (CPU). It is further enhanced with Graphical Processing Unit (GPU) as the GPU has become affordable with the launch of GPU based computing devices. Therefore this paper presents a didactic concept in learning and applying parallel computing with the use of General Purpose Graphical Processing Unit (GPGPU) was carried out and perform preliminary testing in migrating existing sequential codes for solving initially 2D forward modeling of geophysical dataset. There are many challenges in performing these tasks mainly due to lack of some necessary development software tools, but the preliminary findings are promising.Traditionally, 2D and especially 3D forward modeling and inversion of large geophysical datasets are performed on supercomputing clusters. This was due to the fact computing time taken by using PC was too time consuming. With the introduction of parallel computing, attempts have been made to perform computationally intensive tasks on PC or clusters of personal computers where the computing power was based on Central Processing Unit (CPU). It is further enhanced with Graphical Processing Unit (GPU) as the GPU has become affordable with the launch of GPU based computing devices. Therefore this paper presents a didactic concept in learning and applying parallel computing with the use of General Purpose Graphical Processing Unit (GPGPU) was carried out and perform preliminary testing in migrating existing sequential codes for solving initially 2D forward modeling of geophysical dataset. There are many challenges in performing these tasks mainly due to lack of some necessary development software tools, but the preliminary findings are promising

Numerical solution of 3-D electromagnetic problems in exploration geophysics and its implementation on massively parallel computers

The growing significance, technical development and employment of electromagnetic (EM) methods in exploration geophysics have led to the increasing need for reliable and fast techniques of interpretation of 3-D EM data sets acquired in complex geological environments. The first and most important step to creating an inversion method is the development of a solver for the forward problem. In order to create an efficient, reliable and practical 3-D EM inversion, it is necessary to have a 3-D EM modelling code that is highly accurate, robust and very fast. This thesis focuses precisely on this crucial and very demanding step to building a 3-D EM interpretation method. The thesis presents as its main contribution a highly accurate, robust, very fast and extremely scalable numerical method for 3-D EM modelling in geophysics that is based on finite elements (FE) and designed to run on massively parallel computing platforms. Thanks to the fact that the FE approach supports completely unstructured tetrahedral meshes as well as local mesh refinements, the presented solver is able to represent complex geometries of subsurface structures very precisely and thus improve the solution accuracy and avoid misleading artefacts in images. Consequently, it can be successfully used in geological environments of arbitrary geometrical complexities. The parallel implementation of the method, which is based on the domain decomposition and a hybrid MPI-OpenMP scheme, has proved to be highly scalable - the achieved speed-up is close to the linear for more than a thousand processors. Thanks to this, the code is able to deal with extremely large problems, which may have hundreds of millions of degrees of freedom, in a very efficient way. The importance of having this forward-problem solver lies in the fact that it is now possible to create a 3-D EM inversion that can deal with data obtained in extremely complex geological environments in a way that is realistic for practical use in industry. So far, such imaging tool has not been proposed due to a lack of efficient, parallel FE solutions as well as the limitations of efficient solvers based on finite differences. In addition, the thesis discusses physical, mathematical and numerical aspects and challenges of 3-D EM modelling, which have been studied during my research in order to properly design the presented software for EM field simulations on 3-D areas of the Earth. Through this work, a physical problem formulation based on the secondary Coulomb-gauged EM potentials has been validated, proving that it can be successfully used with the standard nodal FE method to give highly accurate numerical solutions. Also, this work has shown that Krylov subspace iterative methods are the best solution for solving linear systems that arise after FE discretisation of the problem under consideration. More precisely, it has been discovered empirically that the best iterative method for this kind of problems is biconjugate gradient stabilised with an elaborate preconditioner. Since most commonly used preconditioners proved to be either unable to improve the convergence of the implemented solvers to the desired extent, or impractical in the parallel context, I have proposed a preconditioning technique for Krylov methods that is based on algebraic multigrid. Tests for various problems with different conductivity structures and characteristics have shown that the new preconditioner greatly improves the convergence of different Krylov subspace methods, which significantly reduces the total execution time of the program and improves the solution quality. Furthermore, the preconditioner is very practical for parallel implementation. Finally, it has been concluded that there are not any restrictions in employing classical parallel programming models, MPI and OpenMP, for parallelisation of the presented FE solver. Moreover, they have proved to be enough to provide an excellent scalability for it

Proceedings of the Second International Workshop on Sustainable Ultrascale Computing Systems (NESUS 2015) Krakow, Poland

Proceedings of: Second International Workshop on Sustainable Ultrascale Computing Systems (NESUS 2015). Krakow (Poland), September 10-11, 2015

The EU Center of Excellence for Exascale in Solid Earth (ChEESE): Implementation, results, and roadmap for the second phase

publishedVersio

Optimization of Finite-Differencing Kernels for Numerical Relativity Applications

A simple optimization strategy for the computation of 3D finite-differencing kernels on many-cores architectures is proposed. The 3D finite-differencing computation is split direction-by-direction and exploits two level of parallelism: in-core vectorization and multi-threads shared-memory parallelization. The main application of this method is to accelerate the high-order stencil computations in numerical relativity codes. Our proposed method provides substantial speedup in computations involving tensor contractions and 3D stencil calculations on different processor microarchitectures, including Intel Knight Landing

Three-dimensional modelling and inversion of controlled source electromagnetic data

The marine Controlled Source Electromagnetic (CSEM) method is an important and almost self-contained discipline in the toolkit of methods used by geophysicists for probing the earth. It has increasingly attracted attention from industry during the past decade due to its potential in detecting valuable natural resources such as oil and gas. A method for three-dimensional CSEM modelling in the frequency domain is presented. The electric field is decomposed in primary and secondary components, as this leads to a more stable solution near the source position. The primary field is computed using a resistivity model for which a closed form of solution exists, for example a homogeneous or layered resistivity model. The secondary electric field is computed by discretizing a second order partial differential equation for the electric field, also referred in the literature as the vector Helmholtz equation, using the edge finite element method. A range of methods for the solution of the linear system derived from the edge finite element discretization are investigated. The magnetic field is computed subsequently, from the solution for the electric field, using a local finite difference approximation of Faraday’s law and an interpolation method. Tests, that compare the solution obtained using the presented method with the solution computed using alternative codes for 1D and 3D synthetic models, show that the implemented approach is suitable for CSEM forward modelling and is an alternative to existing codes. An algorithm for 3D inversion of CSEM data in the frequency domain was developed and implemented. The inverse problem is solved using the L-BFGS method and is regularized with a smoothing constraint. The inversion algorithm uses the presented forward modelling scheme for the computation of the field responses and the adjoint field for the computation of the gradient of the misfit function. The presented algorithm was tested for a synthetic example, showing that it is capable of reconstructing a resistivity model which fits the synthetic data and is close to the original resistivity model in the least-squares sense. Inversion of CSEM data is known to lead to images with low spatial resolution. It is well known that integration with complementary data sets mitigates this problem. It is presented an algorithm for the integration of an acoustic velocity model, which is known a priori, in the inversion scheme. The algorithm was tested in a synthetic example and the results demonstrate that the presented methodology is promising for the improvement of resistivity models obtained from CSEM data

Fast algorithm for real-time rings reconstruction

The GAP project is dedicated to study the application of GPU in several contexts in which real-time response is important to take decisions. The definition of real-time depends on the application under study, ranging from answer time of μs up to several hours in case of very computing intensive task. During this conference we presented our work in low level triggers [1] [2] and high level triggers [3] in high energy physics experiments, and specific application for nuclear magnetic resonance (NMR) [4] [5] and cone-beam CT [6]. Apart from the study of dedicated solution to decrease the latency due to data transport and preparation, the computing algorithms play an essential role in any GPU application. In this contribution, we show an original algorithm developed for triggers application, to accelerate the ring reconstruction in RICH detector when it is not possible to have seeds for reconstruction from external trackers

High-performance tsunami modelling with modern GPU technology

PhD ThesisEarthquake-induced tsunamis commonly propagate in the deep ocean as long waves and develop into sharp-fronted surges moving rapidly coastward, which may be effectively simulated by hydrodynamic models solving the nonlinear shallow water equations (SWEs). Tsunamis can cause substantial economic and human losses, which could be mitigated through early warning systems given efficient and accurate modelling. Most existing tsunami models require long simulation times for real-world applications. This thesis presents a graphics processing unit (GPU) accelerated finite volume hydrodynamic model using the compute unified device architecture (CUDA) for computationally efficient tsunami simulations. Compared with a standard PC, the model is able to reduce run-time by a factor of > 40. The validated model is used to reproduce the 2011 Japan tsunami. Two source models were tested, one based on tsunami waveform inversion and another using deep-ocean tsunameters. Vertical sea surface displacement is computed by the Okada model, assuming instantaneous sea-floor deformation. Both source models can reproduce the wave propagation at offshore and nearshore gauges, but the tsunameter-based model better simulates the first wave amplitude. Effects of grid resolutions between 450-3600 m, slope limiters, and numerical accuracy are also investigated for the simulation of the 2011 Japan tsunami. Grid resolutions of 1-2 km perform well with a proper limiter; the Sweby limiter is optimal for coarser resolutions, recovers wave peaks better than minmod, and is more numerically stable than Superbee. One hour of tsunami propagation can be predicted in 50 times on a regular low-cost PC-hosted GPU, compared to a single CPU. For 450 m resolution on a larger-memory server-hosted GPU, performance increased by ~70 times. Finally, two adaptive mesh refinement (AMR) techniques including simplified dynamic adaptive grids on CPU and a static adaptive grid on GPU are introduced to provide multi-scale simulations. Both can reduce run-time by ~3 times while maintaining acceptable accuracy. The proposed computationally-efficient tsunami model is expected to provide a new practical tool for tsunami modelling for different purposes, including real-time warning, evacuation planning, risk management and city planning