# Power Consumption Comparison of GPU Linear Solvers for Cellular Potts Model Simulations
## 1 Introduction  
Energy consumption is a significant challenge in the sustainability of computational science. The growing energy demands of increasingly complex simulations and algorithms lead to substantial resource use, which conflicts with global sustainability goals. Efficient energy usage is crucial to reduce the environmental impact of computational activities, making energy optimization a key focus in advancing sustainable practices. In the context of modern computational science, energy consumption and waste pose significant challenges. The growing complexity of simulations and the computational demands of advanced algorithms and last-generation computers contribute to increased energy usage [1]. In order to address and reduce the requested large execution times, high-performance computing (HPC) environments are very helpful in several scientific fields [2, 3]. In an HPC context, this issue is intensified due to the large number of processors operating in parallel, usually resulting in elevated energy consumption. Thus, in this sustainability scenario the study of effects of the usage of HPC machine becomes crucial and a fair energy consumption analysis of software and algorithms is mandatory. This paper focuses on the energy consumption of a specific set of parallel implementations of the Cellular Potts model (CPM) simulation by evaluating the impact on the overall energy efficiency. In the context of the cellular behavior field, the CPM represents a useful tool for biological cell simulation which helps the understanding of cell behavior [4, 5]. CPM simulations are useful for improving the knowledge of various diseases and developing related treatments. This topic spans multiple disciplines, including molecular biology, genetics, biochemistry, and biophysics. By examining cellular behavior, the fundamental mechanisms of cellular processes are deeply explored. This knowledge plays a key role to identifying diseases and creating ad hoc therapies, such as those focused on cancer cell behavior. The approach of the Cellular Potts model is mainly based on the minimization of the biological system energy, which is dependent on cell-cell interactions: cell-cell adhesion, cell-substrate adhesion, and cell strain. Due to the need for accurate simulations, the size of the problem heavily impacts the time and energy consumption, leading to the use of parallel approaches. Some attempts in this direction can be found in [6], where the authors use the Message Passing Interface (MPI) in a many-CPUs environment in the study in [7]; an approach based on software transactional memory for task synchronization is used in Ref. [8], where random walk-based algorithms are implemented in parallel. A further parallel implementation, which represents the starting point of this study, is presented in [9]. Here, the authors exploit the computational power of modern graphics processing units (GPUs) in a high-performance computing environment. The algorithm involves several kernels and, among them, the most demanding task lies in solving a large sparse linear system which integrates cell mechanics descriptions through the finite element method (FEM) for the evaluation of the system's biological energy. This parallel implementation uses the Jacobi iterative method solver by ensuring good performance in terms of execution time. The presented works are the main research threads in the field of parallel computing, and here, we report them as a part of storytelling approach. It is important to underline that there are no prior articles that have addressed power consumption. In this paper, we tackle this aspect, comparing it with the most recent parallel software available. A preliminary study of the power consumption of this software was conducted in [10], showing its capability in achieving the low-energy requirement.