scholarly journals Optimizing the Accelerated Recursive Doubling Algorithm for Block Tridiagonal Systems of Equations

2020 ◽  
Author(s):  
Muktaka Joshipura ◽  
Sudip Seal
Keyword(s):  
Systems Of Equations ◽  
Tridiagonal Systems

A symbolic algorithm for periodic tridiagonal systems of equations

2014 ◽  
Vol 52 (8) ◽  
pp. 2222-2233 ◽  
Author(s):  
Ji-Teng Jia ◽  
Qiong-Xiang Kong
Keyword(s):  
Systems Of Equations ◽  
Tridiagonal Systems ◽  
Symbolic Algorithm

Revisiting parallel cyclic reduction and parallel prefix-based algorithms for block tridiagonal systems of equations

2013 ◽  
Vol 73 (2) ◽  
pp. 273-280 ◽  
Author(s):  
Sudip K. Seal ◽  
Kalyan S. Perumalla ◽  
Steven P. Hirshman
Keyword(s):  
Systems Of Equations ◽  
Cyclic Reduction ◽  
Parallel Prefix ◽  
Tridiagonal Systems

An iteration-based hybrid parallel algorithm for tridiagonal systems of equations on multi-core architectures

2015 ◽  
Vol 27 (17) ◽  
pp. 5076-5095 ◽  
Author(s):  
Guangping Tang ◽  
Wangdong Yang ◽  
Kenli Li ◽  
Yu Ye ◽  
Guoqing Xiao ◽  
...  
Keyword(s):  
Parallel Algorithm ◽  
Systems Of Equations ◽  
Tridiagonal Systems

Symplectic factorizations and parallel iterative algorithms for tridiagonal systems of equations

CALCOLO ◽  
1992 ◽  
Vol 29 (3-4) ◽  
pp. 159-191 ◽  
Author(s):  
L. Bergamaschi ◽  
R. Bevilacqua ◽  
P. Zellini
Keyword(s):  
Iterative Algorithms ◽  
Systems Of Equations ◽  
Parallel Iterative Algorithms ◽  
Parallel Iterative ◽  
Tridiagonal Systems

Implicit GPU Accelerated Numerical Simulations via the Use of Ghost Cell Immersed Boundary Method

2020 ◽  
Author(s):  
Piotr Zacharzewski ◽  
Richard Jefferson-Loveday
Keyword(s):  
Immersed Boundary Method ◽  
Memory Access ◽  
Implicit Time ◽  
Immersed Boundary ◽  
Complex Geometries ◽  
Systems Of Equations ◽  
Graphic Processing Units ◽  
Boundary Method ◽  
Access Patterns ◽  
Tridiagonal Systems

Abstract Flow as well as geometry inside turbomachinery components such as turbine blades is complex and difficult to handle accurately. Computationally affordable Reynolds Averaged Navier Stokes (RANS) simulations are often not suitable and partly resolving simulations such as Large Eddy Simulation (LES) or hybrid RANS-LES are needed for sufficient accuracy in the area. Within industrial turbine design, these are not deployed routinely, if at all, due to their presently unaffordable computational cost and time-consuming grid generation for complex geometries. General Purpose Graphic Processing Units (GPGPUs) and other modern heterogeneous hardware offer much cheaper computational power, however, so far remain mostly unharnessed in the field of CFD due to difficulty of creating structured datasets required to utilise the GPUs effectively. While unstructured or hybrid grids can be used on massively parallel platforms, the typically irregular memory access patterns they demand usually prohibits effective scaling and GPU remains mostly idle, negating the benefits. Within CFD, structured datasets with ordered memory access patterns are most easily obtained with structured multiblock grids and such grids are an excellent candidate for GPU platforms. This is not without challenges as creating high quality structured grids over complex geometries is known to be a highly time consuming and difficult process. Another limitation of GPUs is difficulty of solving tridiagonal systems of equations efficiently on those platforms. Solution of such systems of equations is typically required for implicit time advancement or convergence acceleration techniques such as AMG and it is well established that implicit numerical schemes provide significant computational savings due to their efficiency. In the present work a novel Alternating Direction Implicit (ADI) library is integrated into the CFD system to enable scalable solution of tridiagonal systems on GPUs. In the current paper a GPU-accelerated Immersed Boundary Method (IBM) code is presented and validated for turbo-machinery applications. It is shown that the combination of IBM, a high-level Oxford Parallel library for Structured applications (OPS) and an ADI solver provide the geometric as well as computational flexibility unmatched by traditional unstructured solvers. A single source code exists for major hardware platforms and the parallel implementation is decoupled from the scientific codebase, making the code scalable and easily adaptable to any emerging, future architectures.

Base-p-cyclic reduction for tridiagonal systems of equations

1991 ◽  
Vol 8 (2) ◽  
pp. 117-125 ◽  
Author(s):  
Pieter P.N. de Groen
Keyword(s):  
Systems Of Equations ◽  
Cyclic Reduction ◽  
Tridiagonal Systems
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