Eigenvalue and eigenvector computations are fundamental in various scientific and engineering domains. For Structured Population Heterogeneous Models (SPHMs), these computations are crucial for understanding the dynamics and stability of populations with varying structures. Current algorithms primarily focus on Non-Homogeneous Models (NHMs) and Homogeneous Models (HMs), often requiring approximations when applied to SPHMs. There is a clear need for an algorithm specifically tailored to SPHMs to enhance accuracy and efficiency.
The novel algorithm, which forms part of this Innovation Studies, has been designed to compute a subset of the eigenvalues and eigenvectors specific to Structured Population Heterogeneous Models (SPHMs). Utilizing an iterative approach, this algorithm will be systematically compared against standard algorithms for Non-Homogeneous Models (NHMs) and algorithms for Homogeneous Models (HMs), which can often be applied to an approximated version of the SPHM. The comparison will include:
- Serial Execution: Comparison of computation time and accuracy.
- Parallel Execution: Evaluation of performance using MPI and/or GPU acceleration.
The ISOLV-BSE will be incorporated into the Scalable Library for Eigenvalue Problem Computations (SLEPc), thus ensuring public accessibility and a broad distribution within the scientific community. Furthermore, a subroutine for calling the algorithm will be incorporated into the yambo code, which is already interfaced with the SLEPc library. The development of this novel algorithm and its integration within the SLEPc library and yambo code is expected to result in significant advancements in the computational capabilities for SPHMs. This will ensure a seamless integration, allowing users to easily transition to using our algorithm for realistic applications. The algorithm will be implemented within the SLEPc library, ensuring its accessibility to the wider community. The SLEPc library, renowned for its efficacy in addressing large-scale eigenvalue problems, will serve as a robust foundation for our implementation.
The algorithm will provide researchers with a powerful tool for computing eigenvalues and eigenvectors, thereby facilitating the discovery of new insights and applications in the study of structured populations.