Marcin Łoś

TL;DR: Tests and the results of 2-D simulations of melanoma progression clearly show that isogeometric L2 projection utilizing the alternating directions solver is superior over classical approaches in terms of computational complexity, what makes it an excellent candidate for a numerical engine for continuous–discrete models of complex biological systems.

TL;DR: An application of Alternating Direction Implicit algorithm for solution of non-stationary PDE-s using isogeometric finite element method and it is shown that ADI algorithm has a linear computational cost at every time step.

TL;DR: The installation, implementation of exemplary three PDEs, and execution of the simulations on multi-core Linux cluster nodes are described, including heat transfer, linear elasticity, as well as non-linear flow in heterogeneous media.

TL;DR: The method mixes the benefits resulting from isogeometric analysis, implicit dynamics, residual minimization, and alternating direction solver with direction splitting, and shows that the resulting system of linear equations has a Kronecker product structure, which results in a linear computational cost of the direct solver.

TL;DR: High computational efficiency and accuracy of the model is shown, its perfect parallel scalability with the number of CPU cores is demonstrated, and the application of the solver in predictive oncology is discussed.