Optimized Algorithms for Solving Structural Inverse Gravimetry and Magnetometry Problems on GPUs

Akimova, Elena N.; Misilov, Vladimir E.; Tretyakov, Andrey I.

doi:10.1007/978-3-319-67035-5_11

Cited by 8 publications

(4 citation statements)

References 8 publications

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“…To solve the SLAEs with various matrix structures, different numerical methods may be used. In this work, for solving the block-tridiagonal SLAE (11) we will use the blockelimination method [31] and parallel matrix sweep method [32].…”

Section: Numerical Methods For Solving the Slaementioning

confidence: 99%

Parallel Algorithm for Solving the Inverse Two-Dimensional Fractional Diffusion Problem of Identifying the Source Term

Akimova,

Sultanov,

Misilov

et al. 2023

Fractal Fract

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This paper is devoted to the development of a parallel algorithm for solving the inverse problem of identifying the space-dependent source term in the two-dimensional fractional diffusion equation. For solving the inverse problem, the regularized iterative conjugate gradient method is used. At each iteration of the method, we need to solve the auxilliary direct initial-boundary value problem. By using the finite difference scheme, this problem is reduced to solving a large system of a linear algebraic equation with a block-tridiagonal matrix at each time step. Solving the system takes almost the entire computation time. To solve this system, we construct and implement the direct parallel matrix sweep algorithm. We establish stability and correctness for this algorithm. The parallel implementations are developed for the multicore CPU using the OpenMP technology. The numerical experiments are performed to study the performance of parallel implementations.

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Section: Numerical Methods For Solving the Slaementioning

confidence: 99%

Parallel Algorithm for Solving the Inverse Two-Dimensional Fractional Diffusion Problem of Identifying the Source Term

Akimova,

Sultanov,

Misilov

et al. 2023

Fractal Fract

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“…The noise was constructed by adding the field of 512 randomly placed point sources with 10% level of the original field. The Jacobian matrix for this problem is 2 14 × 3 • 2 14 . The smoothing parameter was 𝛽 = 1.2.…”

Section: Test Problemmentioning

confidence: 99%

“…In previous works, [12][13][14][15][16] for solving the problem in the case of multiple layers, we constructed the algorithms based on the steepest descent and the conjugate gradient methods with the weighting factors. These methods allow one to find multiple surfaces from the base equation simultaneously.…”

Section: Introductionmentioning

confidence: 99%

Regularized gradient algorithms for solving the nonlinear gravimetry problem for the multilayered medium

Akimova

Misilov

Sultanov

2020

Math Methods in App Sciences

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We present new numerical algorithms for solving the structural inverse gravimetry problem for the case of multiple surfaces. The inverse problem of finding the multiple surfaces that divide the constant density layers is an ill‐posed one described by a nonlinear integral equation of the first kind. To solve it, it is necessary to apply the regularization ideas. The new regularized variants of the gradient type methods with the weighting factors are constructed, namely, the steepest descent and conjugate gradient method. We suggest the empirical rule for choosing the regularization parameters. On the basis of the constructed methods, we elaborate the parallel algorithms and implement them in the multicore CPU using the OpenMP technology. A set of experiments with the disturbed data is performed to test the gradient algorithms and study performance of the developed code. For the test problems with quasi‐real data, these new regularized algorithms increase the accuracy and speed up computation in comparison with the unregularized ones. By using the 8‐core CPU, we achieve the speedup of 8 times.

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“…Thus, development of the efficient numerical algorithms is a crucially important problem. The promising way to solve various compute-intensive problems is parallel computing [12][13][14][15][16][17][18]. Several parallel algorithms has been developed specifically for the fractional differential equations and anomalous diffusion problems [19,20].…”

Section: Introductionmentioning

confidence: 99%

Parallel Direct and Iterative Methods for Solving the Time-Fractional Diffusion Equation on Multicore Processors

2022

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The work is devoted to developing the parallel algorithms for solving the initial boundary problem for the time-fractional diffusion equation. After applying the finite-difference scheme to approximate the basis equation, the problem is reduced to solving a system of linear algebraic equations for each subsequent time level. The developed parallel algorithms are based on the Thomas algorithm, parallel sweep algorithm, and accelerated over-relaxation method for solving this system. Stability of the approximation scheme is established. The parallel implementations are developed for the multicore CPU using the OpenMP technology. The numerical experiments are performed to compare these methods and to study the performance of parallel implementations. The parallel sweep method shows the lowest computing time.

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Optimized Algorithms for Solving Structural Inverse Gravimetry and Magnetometry Problems on GPUs

Cited by 8 publications

References 8 publications

Parallel Algorithm for Solving the Inverse Two-Dimensional Fractional Diffusion Problem of Identifying the Source Term

Parallel Algorithm for Solving the Inverse Two-Dimensional Fractional Diffusion Problem of Identifying the Source Term

Regularized gradient algorithms for solving the nonlinear gravimetry problem for the multilayered medium

Parallel Direct and Iterative Methods for Solving the Time-Fractional Diffusion Equation on Multicore Processors

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