[1] Marcin Łoś, Judit Munoz-Matute, Ignacio Muga, Maciej Paszyński, Isogeometric Residual Minimization Method (iGRM) with direction splitting for non-stationary advection–diffusion problems, Computers & Mathematics with Applications, 79 (2) (2020) 213-229

This paper describes ultra-fast linear computational cost solver O(N) for numerical simulations of difficult advection dominated diffusion problem, which requires special stabilization method. We provide a detailed mathematical derivation of the new numerical method which we call "isogeometric Residual Minimization (iGRM)".

https://www.sciencedirect.com/science/article/pii/S0898122119303268

[2] Vladimir Puzyrev, Marcin Łoś, Grzegorz Gurgul, Victor Calo, Witold Dzwinel, Maciej Paszyński, Parallel splitting solvers for the isogeometric analysis of the Cahn-Hilliard equation, Computer Methods in Biomechanics and Biomedical Engineering, 22(16) (2019) 1269-1281

This paper describes ulta-fast linear computational cost solver for numerical solution of Cahn-Hilliard equations. The solver allows for efficient simulations with applications to material science and tumor progression simulatons.

https://www.tandfonline.com/doi/abs/10.1080/10255842.2019.1661388

[3] Marcin Łoś, Adrian Kłusek, Muhammad Amber Hassaan, Keshav Pingali, Witold Dzwinel, Maciej Paszyński, Parallel fast isogeometric L2 projection solver with GALOIS system for 3D tumor growth simulations, Computer Methods in Applied Mechanics and Engineering, 343 (1) (2019) 1-22

This work describes the mathematical model of tumor progression and regression and a fast parallel solver with a linear computational cost for performing computer simulations. Such simulations performed on a laptop allows for computer visualizations of tumor tissue density, angiogenic enzyme concentration, and growth of blood vessel networks in the area of tumor tissue growth. Simulation code is available in Open Source mode.

https://www.sciencedirect.com/science/article/pii/S0045782518304341

[4] Leszek Siwik, Maciej Woźniak, Marcin Łoś, Maciej Paszyński, Fast and green parallel isogeometric analysis computations for multi-objective optimization of liquid fossil fuel reserve exploitation with minimal groundwater contamination, Journal of Parallel and Distributed Computing, 13 (2019) 89-103

This paper describes the computational framework for simulations of environmental aspects of the oil/gas exploration process. We also propose the optimization methodology for both minimization of the ground water contamination, as well as the algorithms for minimization of the computational cost and energy consumption of the computer simulations.

https://www.sciencedirect.com/science/article/abs/pii/S0743731518306890

[5] Leszek Siwik, Marcin Los, Adrian Klusek, Keshav Pingali, Witold Dzwinel, Maciej Paszynski, Supermodeling of tumor dynamics with parallel isogeometric analysis solver, https://arxiv.org/abs/1912.12836

In this paper we propose a data assimilation technique called supermodeling for tuning of the three-dimensional tumor growth simulations. We couple several tumor models to match the volume of the simulated and measured tumor, progressing with time.

https://arxiv.org/abs/1912.12836

[6] Marcin Łoś, Maciej Woźniak, Maciej Paszyński, Andrew Lenharth, Muhamm Amber Hassaan, Keshav Pingali, IGA-ADS: isogeometric analysis FEM using ADS solver, Computer Physics Communications, 217 (2017) 99-116, DOI: 10.1016/j.cpc.2017.02.023

This paper describes application of the Alternating Direction Solver to simulation of non-stationary processes by using an explicit time discretization scheme and treating the simulation as a series of L2-projection problems. An implementation of this idea - IGA-ADS C++ library using GALOIS framework for shared-memory parallelization - is presented as well.

https://www.sciencedirect.com/science/article/pii/S0010465517300759

[7] Marcin Łoś, Robert Schaefer, Maciej Paszyński, Parallel space-time hp-adaptive discretization scheme for parabolic problems, Journal of Computational and Applied Mathematics, 344 (2018) 819-835, DOI:10.1016/j.cam.2017.12.005

This paper describes an algorithm for simulating non-stationary processes that allows carrying out space adaptation for consecutive time steps in parallel. The algorithm is presented as a multi-agent system where each calculations in time step are performed by different agent. Analysis of the error propagation and numerical results using hp-adaptive FEM are also included.

https://www.sciencedirect.com/science/article/abs/pii/S0377042717306192

[8] Jakub Sawicki, Marcin Łoś, Maciej Smołka, Julen Alvarez-Aramberri, Using Covariance Matrix Adaptation Evolutionary Strategy to boost the search accuracy in hierarchic memetic computations, Journal of Computational Science, 34 (2019) 48-54, DOI: 10.1016/j.jocs.2019.04.005

This paper presents an enhancement of the populational HMS (Hierarchical Memetic Strategy) global optimization algorithm by augmenting its local phase with CMA-ES - a stochastic algorithm which mimics some aspects of evolutionary algorithms without explicitly working with populations. This approach is compared with using the standard evolutionary algorithm SEA in the local phase.

https://www.sciencedirect.com/science/article/abs/pii/S1877750318307233

[9] Marcin Łoś, Pouria Behnoudfar, M. Paszyński, V. M. Calo, Fast isogeometric solvers for hyperbolic wave propagation problems, Computers and Mathematics with Applications, 80 (1) (2020) 109-120, DOI: 10.1016/j.camwa.2020.03.002

This paper presents an application of Alternating Direction Solver (ADS) to simulating hyperbolic wave propagation. Space is discretized using Isogeometric Analysis, and the time discretization is carried out using a novel unconditionally stable implicit scheme such that the resulting matrix can be approximately represented as a Kronecker product, which allows using ADS. Numerical results for P-wave propagation and linear elasticity are presented.

https://www.sciencedirect.com/science/article/pii/S0898122120300997

[10] Piotr Faliszewski, Jakub Sawicki, Robert Schaefer, Maciej Smołka, Multiwinner voting in genetic algorithms. IEEE Intelligent Systems, 32(1) (2017) 40-48, DOI:10.1109/MIS.2017.5

In the paper we show a solution to maintain population diversity when solving problems with insensitivity (lowland) regions in the objective function. We extend a Simple Evolutionary Algorithm (SEA) with a selection mechanism based on multi-winner election, stemming from game

theory.

https://ieeexplore.ieee.org/document/7851129

[11] Jakub Sawicki, Marcin Łoś, Maciej Smołka, Robert Schaefer, Julen Álvarez-Aramberri, Approximating landscape insensitivity regions in solving ill-conditioned inverse problems, Memetic Computing, 10(3) (2018) 279-289, DOI:10.1007/s12293-018-0258-5

We show a complex meta-heuristic method which identifies insensitivity (lowland) regions in the objective function. This shape approximation strategy uses, among other methods, a multi-winner elections based evolutionary algorithm and a B-spline based local approximation.

https://link.springer.com/article/10.1007/s12293-018-0258-5

[12] Smołka Maciej, Gajda-Zagórska Ewa, Schaefer Robert, Paszyński Maciej, Pardo David, A hybrid method for inversion of 3D AC logging measurements, *Applied Soft Computing*, 36 (2015) 422-456, DOI: 10.1016/j.asoc.2015.06.055

The paper presents a new method of solving inverse parametric problems of exploring hydrocarbon resources by inverting the AC logging measurements. The hybrid memetic strategy with adaptive accuracy, coupled with the hp-FEM solver for the dual forward problem of nonstationary Maxwell equation was applied. The rule of optimal common forward and inverse error scaling was formulated and proved. The proposed strategy was applied to the sample engineering problem.

https://dl.acm.org/doi/abs/10.1016/j.asoc.2015.06.055

[13] Gajda-Zagórska Ewa, Schaefer Robert, Smołka Maciej, Pardo David, Álvarez-Aramberri Julen, A Multi-objective Memetic Inverse Solver Reinforced by Local Optimization Methods. *Journal of Computational Science*, 18 (2017) 85-94, DOI: 10.1016/j.jocs.2016.06.007

The paper introduces the new complex strategy of solving Pareto problems. It is composed of two components: the hierarchic memetic strategy equipped with the MOEA selection and the refinement procedure which consists in running many convex optimization processes based on the local criteria scalarization. The benchmarks exhibit the advantage of a proposed method over a traditional approach.

https://www.sciencedirect.com/science/article/abs/pii/S1877750316301089

[14] Schaefer Robert, Łoś Marcin, Sieniek Marcin, Demkowicz Leszek, Paszyński Maciej, Quasi-liniear computational cost adaptive solvers for three dimensional modeling of heating of a human head induced by cell-phone, *Journal of Computational Sciences*, 11 (2015) 163-174, DOI: 10.1016/j.jocs.2015.09.009

The new algorithm for solving of challenging adaptive time-dependent problems with Crank-Nicolson kind of time integration in parallel is proposed. It allows for parallel execution of computations from different time steps. The algorithm was tested on the challenging computational problem, which is the solution of the Pennes equation over a human head. The heat source intensity was obtained by approximation of the solution of the Maxwell equation computed over the model of human head.

https://www.sciencedirect.com/science/article/abs/pii/S1877750315300235

[15] Leszek Siwik, Maciej Woźniak, Victor Trujillo, David Pardo, Victor Manuel Calo, Maciej Paszyński, Parallel refined isogeometric analysis in 3D, IEEE Transactions on Parallel and Distributed Systems, 30(5) (2019) 1134-1142

This paper describes refined Isogeometric Analysis (rIGA) method, which improves the sequential execution of direct solvers. The refinement strategy enriches traditional highly-continuous IGA spaces by introducing low-continuity hyperplanes along the boundaries of certain pre-defined macro-elements. We propose a solution strategy for rIGA for parallel distributed memory machines and compare the computational costs of solving rIGA versus IGA discretizations.

https://ieeexplore.ieee.org/document/8523633

[16] Maciej Paszyński, Leszek Siwik, Maciej Woźniak, Concurrency of three-dimensional refined isogeometric analysis, Parallel Computing, 80 (2018) 1-22

In this paper we perform the analysis of the concurrency of the parallel refined Iso-geometric Analysis (rIGA) computations. We use the trace theory approach to identify the sets of tasks that can be executed in concurrent, one set after the other. We also estimate the computational cost of the tasks. Finally we perform numerical experiments on the representative three-dimensional meshes partitioned into macro-elements with quadratic and cubic B-splines, and compare the numerical results with theoretical estimates.

https://www.sciencedirect.com/science/article/abs/pii/S0167819118300875

[17] Maciej Woźniak, Marcin Łoś, Maciej Paszyński, Lisandro Dalcin, Victor Manuel Calo, Parallel fast isogeometric solvers for explicit dynamics, Computing and Informatics, 36(2) (2017) 423-448

This paper presents a parallel implementation of the fast isogeometric solvers for explicit dynamics for solving non-stationary time-dependent problems. The algorithm is described in pseudo-code. We present theoretical estimates of the computational and communication complexities for a single time step of the parallel algorithm.

W tym artykule przedstawiamy równoległą implementację szybkiego solwera izogeometrycznego do rozwiązywania niestacjonarnych problemów zależnych od czasu. Algorytm jest opisany w pseudokodzie. Prezentujemy teoretyczne szacowania złożoności obliczeniowej i komunikacyjnej dla pojedynczego kroku czasowego algorytmu równoległego.

http://www.cai.sk/ojs/index.php/cai/article/view/2017_2_423

[18] Ignacio Martinez-Fernandez, Maciej Woźniak, Luis E. Garcia-Castillo, Maciej Paszyński, Mesh-based multi-frontal solver with reuse of partial LU factorizations for antenna array, Journal of Computational Science, 18 (2017) 132-142

In this paper we advocate new approach computational problem, based on the additional knowledge of the structure of the computational mesh. We propose a wrapper over a multi-frontal solver that partitions the computational problem into a cascade of sub-problems, for which a traditional multi-frontal solver is called and asked for the Schur complements.

https://www.sciencedirect.com/science/article/abs/pii/S1877750316302083