Heterogeneous and distributed systems are increasingly used today to speed up the solution of complex computational tasks and to solve previously unsolvable problems. Today's trend shows that of the 500 most powerful supercomputers in the world, 133 are already heterogeneous, meaning that in addition to traditional processors (CPUs), they are equipped with various accelerators, today's most popular graphics processing units (GPUs). It is expected that the future exascale supercomputers, i.e. computers that can perform more than 10^18 operations per second, will also be based on accelerators. Due to their large heterogeneity, the development of efficient and scalable algorithms and applications that achieve high utilisation of such systems is of utmost importance.

The aim of this project is to develop new and improve existing computational methods and algorithms of numerical linear algebra that are able to exploit large heterogeneous systems while achieving very high performance. The main directions of the research are:

• increasing the scalability of the algorithms (increasing the problem size and the number of computational resources),
• reducing the communication overhead and exploiting the complex memory hierarchies of the heterogeneous systems,
• In addition, new models for optimising the parameters of algorithms with respect to the architecture of the underlying computer systems and problem size are being explored in order to reduce the overall execution time,
• the research results obtained will be used in solving large-scale, real-world computational problems in other scientific fields such as computational chemistry, materials physics and molecular medicine.

The project will contribute to the efficient parallelisation and optimisation of algorithms for future heterogeneous and distributed systems and will strengthen research in high-performance computing at the Ruđer Bošković Institute and in the Republic of Croatia.