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Chapter and Conference Paper
Performance Analysis of Direct Gaussian Solvers for Solving 2D Elastodynamic Problem of a Finite-Sized Solid Containing Cavities on CPUs and MICs
The subject of this study is to evaluate the performance of direct Gaussian solvers from Intel®’s MKL and the free PLASMA libraries for a 2D elastodynamic problem, containing cavities/inclusions. Several high per...
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Chapter and Conference Paper
Performance Analysis of a Parallel Hierarchical Semi-separable Compression Solver in Shared and Distributed Memory Environment for BEM Discretization of Flow Around Airfoils
We study the performance of a hierarchical semi-separable compression solver for dense systems of linear algebraic equations arising from boundary elements (BEM) discretization of a 2D laminar flow around airf...
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Chapter and Conference Paper
Spectral Fractional Laplacian with Inhomogeneous Dirichlet Data: Questions, Problems, Solutions
In this paper we discuss the topic of correct setting for the equation \((-\varDelta )^s u=f\) ...
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Chapter
Performance Analysis of Intel Xeon Phi MICs and Intel Xeon CPUs for Solving Dense Systems of Linear Algebraic Equations: Case Study of Boundary Element Method for Flow Around Airfoils
The presented analysis is based on simulation of laminar flows around airfoils. The Boundary Element Method is applied for the numerical solution of the related integral equations. The most computationally exp...
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Chapter and Conference Paper
Numerical Homogenization of Epoxy-Clay Composite Materials
The numerical homogenization of anisotropic linear elastic materials with strongly heterogeneous microstructure is studied. The developed algorithm is applied to the case of two-phase composite material: epoxy...
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Chapter and Conference Paper
Numerical Homogenization of Heterogeneous Anisotropic Linear Elastic Materials
The numerical homogenization of anisotropic linear elastic materials with strongly heterogeneous microstructure is studied. The developed algorithm is applied to the case of trabecular bone tissue. In our prev...
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Chapter and Conference Paper
Calibration of Parameters for Radio-Frequency Ablation Simulation
We consider the simulation of the thermal and electrical processes, involved in the radio-frequency (RF) ablation procedure. RF ablation is a low invasive technique for the treatment of hepatic tumors, utilizi...
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Chapter and Conference Paper
Robust Algebraic Multilevel Preconditioners for Anisotropic Problems
We present an overview on the state of the art of robust AMLI preconditioners for anisotropic elliptic problems. The included theoretical results summarize the convergence analysis of both linear and nonlinear...
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Chapter and Conference Paper
Improving the Efficiency of Parallel FEM Simulations on Voxel Domains
In this work, we consider large-scale finite element modeling on voxel grids. We are targeting the IBM Blue Gene/P computer, which features a 3D torus interconnect. Our previous parallelization approach was to...
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Chapter and Conference Paper
On the Robustness of Two-Level Preconditioners for Quadratic FE Orthotropic Elliptic Problems
We study the construction of subspaces for quadratic FEM orthotropic elliptic problems with a focus on the robustness with respect to mesh and coefficient anisotropy. In the general setting of an arbitrary ell...
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Chapter and Conference Paper
Finite Volume Discretization of Equations Describing Nonlinear Diffusion in Li-Ion Batteries
Numerical modeling of electrochemical process in Li-Ion battery is an emerging topic of great practical interest. In this work we present a Finite Volume discretization of electrochemical diffusive processes o...
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Article
Multilevel algorithms for Rannacher–Turek finite element approximation of 3D elliptic problems
Generalizing the approach of a previous work of the authors, dealing with two-dimensional (2D) problems, we present multilevel preconditioners for three-dimensional (3D) elliptic problems discretized by a fami...
