In this paper we implemented an adaptive mesh refinement in high performance computing environment to study a wide range of problems in engineering. They are nonlinear Fisher-Kolmogorov equation, heat equation, advection equation and poisons equation using traditional message passing interface (MPI). We used adaptive mesh refinement library called AMReX for computation. AMReX is a numerical library containing the functionality to write massively parallel, block-structured adaptive mesh refinement (AMR) applications. Our study includes examples to solve poisons equation in traditional MPI approach and compared the performance between the two methods.