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Michał Mika, M.Sc.

Ph.D. candidate, Computational methods for cavitating flows

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  • school M.Sc. Computational Methods in Engineering, Leibniz Universität Hannover
  • school B.Sc. Computergestützte Ingenieurwissenschaften, Leibniz Universität Hannover

Research interests

isogeometric analysis, efficient numerical methods, software development


I've studied computational engineering science and I'm currently a Ph.D. student at Technische Universität Darmstadt, where I work on efficient isogeometric methods with application to cavitation problems. Here I host my projects and student works. If you've found any mistakes, have questions or suggestions, please let me know at hzkn22@mika.sh.


Matrix-free polynomial preconditioning of saddle point systems using the hyper-power method

M.L. Mika, M.F.P. ten Eikelder, D. Schillinger and R.R. Hiemstra

November 12, 2023;


This study explores the integration of the hyper-power sequence, a method commonly employed for approximating the Moore-Penrose inverse, to enhance the effectiveness of an existing preconditioner. The approach is closely related to polynomial preconditioning based on Neumann series. We commence with a state-of-the-art matrix-free preconditioner designed for the saddle point system derived from isogeometric structure-preserving discretization of the Stokes equations. Our results demonstrate that incorporating multiple iterations of the hyper-power method enhances the effectiveness of the preconditioner, leading to a substantial reduction in both iteration counts and overall solution time for simulating Stokes flow within a 3D lid-driven cavity. Through a comprehensive analysis, we assess the stability, accuracy, and numerical cost associated with the proposed scheme.

Connecting continuum poroelasticity with discrete synthetic vascular trees for modeling liver tissue

A. Ebrahem, E. Jessen, M.F.P. ten Eikelder, T. Gangwar, M. Mika and D. Schillinger

June 12, 2023;


Computational simulations have the potential to assist in liver resection surgeries by facilitating surgical planning, optimizing resection strategies, and predicting postoperative outcomes. The modeling of liver tissue across multiple length scales constitutes a significant challenge, primarily due to the multiphysics coupling of mechanical response and perfusion within the complex multiscale vascularization of the organ. In this paper, we present a modeling framework that connects continuum poroelasticity and discrete vascular tree structures to model liver tissue across disparate levels of the perfusion hierarchy. The connection is achieved through a series of modeling decisions, which include source terms in the pressure equation to model inflow from the supplying tree, pressure boundary conditions to model outflow into the draining tree, and contact conditions to model surrounding tissue. We investigate the numerical behaviour of our framework and apply it to a patient-specific full-scale liver problem that demonstrates its potential to help assess surgical liver resection procedures.

A matrix-free macro-element variant of the hybridized discontinuous Galerkin method

V. Badrkhani, R.R. Hiemstra, M.L. Mika and D. Schillinger

February 17, 2023;

International Journal for Numerical Methods in Engineering

We investigate a macro-element variant of the hybridized discontinuous Galerkin (HDG) method, using patches of standard simplicial elements that can have non-matching interfaces. Coupled via the HDG technique, our method enables local refinement by uniform simplicial subdivision of each macro-element. By enforcing one spatial discretization for all macro-elements, we arrive at local problems per macro-element that are embarrassingly parallel, yet well balanced. Therefore, our macro-element variant scales efficiently to n-node clusters and can be tailored to available hardware by adjusting the local problem size to the capacity of a single node, while still using moderate polynomial orders such as quadratics or cubics. Increasing the local problem size means simultaneously decreasing, in relative terms, the global problem size, hence effectively limiting the proliferation of degrees of freedom. The global problem is solved via a matrix-free iterative technique that also heavily relies on macro-element local operations.

A comparison of matrix-free isogeometric Galerkin and collocation methods for Karhunen–Loève expansion

M.L. Mika, R.R. Hiemstra, T.J.R. Hughes and D. Schillinger

March 13, 2022;

Current Trends and Open Problems in Computational Mechanics

Numerical computation of the Karhunen–Loève expansion is computationally challenging in terms of both memory requirements and computing time. We compare two state-of-the-art methods that claim to efficiently solve for the K–L expansion: (1) the matrix-free isogeometric Galerkin method using interpolation based quadrature proposed by the authors in [1] and (2) our new matrix-free implementation of the isogeometric collocation method proposed in [2]. Two three-dimensional benchmark problems indicate that the Galerkin method performs significantly better for smooth covariance kernels, while the collocation method performs slightly better for rough covariance kernels.

A matrix-free isogeometric Galerkin method for Karhunen-Loève approximation of random fields using tensor product splines, tensor contraction and interpolation based quadrature

M.L. Mika, T.J.R. Hughes, D. Schillinger, P. Wriggers and R.R. Hiemstra

February 9, 2021;

Computer Methods in Applied Mechanics and Engineering

The Karhunen-Loève series expansion decomposes a Gaussian stochastic process into an infinite series of pairwise uncorrelated random variables and pairwise L2 orthogonal functions. The computational complexity of standard Galerkin finite element formation and assembly techniques, as well as memory requirements of direct solution techniques become quickly computationally intractable with increasing polynomial degree and the number of elements. In this work we present a novel matrix-free solution strategy that scales optimally with the problem size, is indepedent of the polynomial degree and is emberassingly parallel. A high-order three-dimensional benchmark illustrates exceptional computational performance combined with high accuracy and robustness.

Electrostatic sensor modeling for torque measurements

M.L. Mika, M. Dannert, F. Mett, H. Weber, W. Mathis and U. Nackenhorst

September 21, 2017;

Advances in Radio Science

Based on a simple draft of an exemplary measurement setup, this paper discusses the general idea behind an electrostatic capacitive torque sensor. For better understanding of the working principle of the sensor the electrostatics, the geometry and the mechanics of the considered measurement setup are modeled. (undergraduate student project)

Visualization of finite element analysis results on 3D printed models

M.L. Mika, K. Dees and U. Nackenhorst

April 14, 2017;

This project explores the possibilities of visualization of finite element analysis results using 3D printed models. By outer-surface extraction and implementation of a VRML interface the interpolated datasets are prepared for a 3D print. (undergraduate student project)