This book constitutes the thoroughly refereed post-conference proceedings of the 13th International Conference on High Performance Computing in Computational Science, VECPAR 2018, held in Sao Pedro, Brazil, in September 2018. The 17 full papers and one short paper included in this book were carefully reviewed and selected from 32 submissions presented at the conference. The papers cover the following topics: heterogeneous systems, shared memory systems and GPUs, and techniques including domain decomposition, scheduling and load balancing, with a strong focus on computational science applications.