The International Conference on Computational Science is an annual conference that brings together researchers and scientists from mathematics and computer science as basic computing disciplines, researchers from various application areas who are pioneering computational methods in sciences such as physics, chemistry, life sciences, and engineering, as well as in arts and humanitarian fields, to discuss problems and solutions in the area, to identify new issues, and to shape future directions for research. ICCS 2013 in Barcelona will be the thirteenth in this series of highly successful conferences. For the previous twelve meetings see: http://www.iccs-meeting.org/iccs2013/previous-iccs.html Since its inception in 2001, ICCS has attracted increasingly higher quality and numbers of attendees and papers. Average attendance each year is about 350 participants. The proceedings series have become a major intellectual resource for computational science researchers and serve to both define and advance the state of the art of the field. Out of the submitted papers to main track and workshops, we will select some 30% high-quality papers for presentation at the conference and publication in the proceedings. These are published by Elsevier in their new Procedia Computer Science series. ICCS is well known for its excellent line up of keynote speakers. The theme for ICCS 2013 is "Computation at the Frontiers of Science", to mark the ever-increasing importance of and progress in computational science theory and practice at the frontiers of science. The conference will be a unique event focusing on recent developments in computational methods for modelling complex systems in diverse areas of science, scalable scientific algorithms, advanced software tools, computational grids, advanced numerical methods. Novel application areas where the above models, algorithms and tools can be efficiently applied such as physical systems, computational and systems biology, environmental systems, finance, but also humanities and socio-economic systems will be considered. ICCS2013 will also feature the important advances in computational science towards exascale computing.