Overview

This library is for both single and many tridiagonal systems of equations. The main algorithm for a tridiagonal matrix consists of the following five steps:

• (1) Transform the partitioned submatrices in the tridiagonal systems into modified submatrices: Each computing core transforms the partitioned submatrices in the tridiagonal systems of equations into the modified forms by applying modified Thomas algorithm.
• (2) Construct reduced tridiagonal systems from the modified submatrices: The reduced tridiagonal systems are constructed by collecting the first and last rows of the modified submatrices from each core using MPI_Ialltoallw.

Features

Single and many tridiagonal system

Single tridiagonal system

• A communication method using MPI_Gather for a single diagonal system.
• \(\texttt{PaScaL_TDMA_plan_single_create}\): A subroutine to create a type variable of \(\texttt{plan_single}\), for a single tridiagonal system
• \(\texttt{PaScaL_TDMA_plan_single_destroy}\): A subroutine to dellocate the \(\texttt{plan_single}\) and all associated data
• \(\texttt{PaScaL_TDMA_plan_single_solve}\): A subroutine for solving a single tridiagonal system with the \(\texttt{MPI_gather}\) and \(\texttt{MPI_scatter}\) fuctions, as shown in upper figure

Many tridiagonal system

• The present method using MPI_Alltoall for many tridiagonal systems.
• \(\texttt{PaScaL_TDMA_plan_many_create}\): A subroutine to create a type variable of \(\texttt{plan_many}\), for a many tridiagonal systems. The definition of the derived data type depends on the version of MPI library.
• \(\texttt{PaScaL_TDMA_plan_many_destroy}\): A subroutine to dellocate the \(\texttt{plan_many}\) and all associated data
• \(\texttt{PaScaL_TDMA_plan_many_solve}\): A subroutine for solving a many tridiagonal systems with the \(\texttt{MPI_Alltoallw}\) fuction, as shown in upper figure

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Credits

Special thanks to all the contributors: