The goal of HighPerMeshes is to develop a practically usable domain-specific framework for the efficient, parallel and scaling implementation of iterative algorithms on unstructured grids. Simulation software in the time domain, that falls into this category (e.g. TD-FEM, TD-DG, network simulations), has increasingly been used in scientific and industrial domains in recent years and complements or supplements comparable methods on structured grids. With the results of this project, developers can with moderate effort extend existing source codes in high-level languages by domain-specific library and language elements. The intelligent compiler infrastructure uses domain knowledge to enable performance optimized, highly parallel execution on all relevant modern hardware architectures (Multicore, Manycore, GPU, FPGA), also in heterogeneous systems. Thus, the project offers to many HPC developers from science and industry an easy and sustainable path towards scaling usage of the most efficient current and future target architectures.