Sixth order compact multi-phase block-AGE iteration methods for computing 2D Helmholtz equation
We discuss sixth order accurate 9-point compact 2- and 3-phase block alternating group explicit (block-AGE) iteration methods for computing 2D Helmholtz equation. We use Dirichlet boundary conditions and no fictitious points are involved outside the solution region for computation. The proposed 2- a...
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| Format: | Article |
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Elsevier
2024-06-01
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| Series: | MethodsX |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2215016124000876 |
| _version_ | 1797272462053867520 |
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| author | R.K. Mohanty Niranjan |
| author_facet | R.K. Mohanty Niranjan |
| author_sort | R.K. Mohanty |
| collection | DOAJ |
| description | We discuss sixth order accurate 9-point compact 2- and 3-phase block alternating group explicit (block-AGE) iteration methods for computing 2D Helmholtz equation. We use Dirichlet boundary conditions and no fictitious points are involved outside the solution region for computation. The proposed 2- and 3-phase block-AGE methods require only two and three sweeps for computation and the error analysis of the suggested approximation is analyzed. We have compared the 2- and 3-phase block-AGE iteration methods with the corresponding block successive over relaxation (block-SOR) method in three experiments, in regard to number of iterations required for convergence and cpu time, where the importance of the role performed by optimal relaxation parameters of the proposed block-AGE iteration methods become evident in stipulating the convergence and precision of the calculated results. In all cases we use the tridiagonal solver and obtain the optimal relaxation parameters through computation. |
| first_indexed | 2024-03-07T14:28:42Z |
| format | Article |
| id | doaj.art-0d06507fa16447568efe5f8b7a63ca65 |
| institution | Directory Open Access Journal |
| issn | 2215-0161 |
| language | English |
| last_indexed | 2024-03-07T14:28:42Z |
| publishDate | 2024-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | MethodsX |
| spelling | doaj.art-0d06507fa16447568efe5f8b7a63ca652024-03-06T05:27:07ZengElsevierMethodsX2215-01612024-06-0112102633Sixth order compact multi-phase block-AGE iteration methods for computing 2D Helmholtz equationR.K. Mohanty0 Niranjan1Corresponding author.; Department of Mathematics, South Asian University, Rajpur Road, Maidan Garhi, New Delhi 110068, IndiaDepartment of Mathematics, South Asian University, Rajpur Road, Maidan Garhi, New Delhi 110068, IndiaWe discuss sixth order accurate 9-point compact 2- and 3-phase block alternating group explicit (block-AGE) iteration methods for computing 2D Helmholtz equation. We use Dirichlet boundary conditions and no fictitious points are involved outside the solution region for computation. The proposed 2- and 3-phase block-AGE methods require only two and three sweeps for computation and the error analysis of the suggested approximation is analyzed. We have compared the 2- and 3-phase block-AGE iteration methods with the corresponding block successive over relaxation (block-SOR) method in three experiments, in regard to number of iterations required for convergence and cpu time, where the importance of the role performed by optimal relaxation parameters of the proposed block-AGE iteration methods become evident in stipulating the convergence and precision of the calculated results. In all cases we use the tridiagonal solver and obtain the optimal relaxation parameters through computation.http://www.sciencedirect.com/science/article/pii/S2215016124000876Block-AGE Multi-stage Iteration Method |
| spellingShingle | R.K. Mohanty Niranjan Sixth order compact multi-phase block-AGE iteration methods for computing 2D Helmholtz equation MethodsX Block-AGE Multi-stage Iteration Method |
| title | Sixth order compact multi-phase block-AGE iteration methods for computing 2D Helmholtz equation |
| title_full | Sixth order compact multi-phase block-AGE iteration methods for computing 2D Helmholtz equation |
| title_fullStr | Sixth order compact multi-phase block-AGE iteration methods for computing 2D Helmholtz equation |
| title_full_unstemmed | Sixth order compact multi-phase block-AGE iteration methods for computing 2D Helmholtz equation |
| title_short | Sixth order compact multi-phase block-AGE iteration methods for computing 2D Helmholtz equation |
| title_sort | sixth order compact multi phase block age iteration methods for computing 2d helmholtz equation |
| topic | Block-AGE Multi-stage Iteration Method |
| url | http://www.sciencedirect.com/science/article/pii/S2215016124000876 |
| work_keys_str_mv | AT rkmohanty sixthordercompactmultiphaseblockageiterationmethodsforcomputing2dhelmholtzequation AT niranjan sixthordercompactmultiphaseblockageiterationmethodsforcomputing2dhelmholtzequation |