Robert Dyja
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Analyzing the Impact of Population Size in AI-Based Reconstruction of the Thermal Parameter in Heat Conduction Modeling Open
The research shows how to use swarming algorithms to rebuild the heat transfer coefficient, especially in regard to the continuous border condition. The authors utilized their application software to do numerical computations, employing cl…
Solving fluid flow problems in space-time with multiscale stabilization: formulation and examples Open
We present a space-time continuous-Galerkin finite element method for solving incompressible Navier-Stokes equations. To ensure stability of the discrete variational problem, we apply ideas from the variational multi-scale method. The fini…
Using artificial intelligence algorithms to reconstruct the heat transfer coefficient during heat conduction modeling Open
The article shows the usage of swarming algorithms for reconstructing the heat transfer coefficient regarding the continuity boundary condition. Numerical calculations were performed using the authors’ own application software with classic…
Space-time finite element analysis of the advection-diffusion equation using Galerkin/least-square stabilization Open
We present a full space-time numerical solution of the advection-diffusion equation using a continuous Galerkin finite element method on conforming meshes. The Galerkin/least-square method is employed to ensure stability of the discrete va…
Impact of input parameters on numerical calculations optimized by swarming algorithms during computer simulations of the heat conduction phenomenon Open
Journal of Applied Mathematics and Computational Mechanics, Prace Naukowe Instytutu Matematyki i Informatyki, Politechnika Częstochowska, Scientific Research of the Institute of Mathematics and Computer Science, Czestochowa University of T…
Selection of the Heat Transfer Coefficient Using Swarming Algorithms Open
The article presents the use of swarming algorithms in selecting the heat transfer coefficient, taking into account the boundary condition of the IV types. Numerical calculations were made using the proprietary TalyFEM program and classic …
Influence of Heat Exchange with Environment on the Results of Heat Transfer Simulations in Periodic Surface Structures Open
The presented paper focuses on a problem of heat transfer in periodic surface structures.The periodic structure surfaces are the compound structures described by mathematical formulas that represent areas similar to porous structures.The i…
Impact of Geometry on the Thermal and Mechanical Properties of Periodic Surface Structures: A Numerical Study Open
Periodic Surface Structures (PSS) fabricated via Additive Manufacturing (AM) have recently emerged as being appropriate candidates for high-value engineered structures. Among the many PSS designs, gyroid structures have demonstrated merits…
Comparison of Results from In-House Solidification Convection Model with Standard Benchmark Open
This paper focuses on a problem of solidification with convection.The performance of a developed model against a standard benchmark of solidification commonly found in literature is presented.The developed model is based on the Navier-Stok…
Heat Conduction in Complex Geometric Structures on Example of Neovius Periodic Surface Open
Heat conduction is an important problem in additive manufacturing, which is the main source of interest for periodic surface structures.The high energy flux, which is required for additive manufacturing to work properly, results in large t…
A Numerical Study of Geometry’s Impact on the Thermal and Mechanical Properties of Periodic Surface Structures Open
The paper focuses on thermal and mechanical analysis of Periodic Surface Structure (PSS). PSS is a continuous surface with a specific topology that is mathematically formulated by geometric factors. Cubic P-surface (“primitive”), D-surface…
3D simulations of solidification with liquid phase flow Open
The work discusses issues related to 3D coagulation simulations including liquid phase flow. The approach chosen by the authors is based on the numerical solution of the enthalpy solidification formula and the Navier-Stokes equation, in wh…
Modeling of heat flow using commercial and authorial software on the example of a permanent magnet motor Open
The aim of the work is the modeling of the heat flow in an electric motor with permanent magnets with a height of 56mm. Numerical calculations were carried out for a simplified 3D model prepared in the Autodesk Inventor solid modeling prog…
Stress analysis in solid-liquid parts of solidifying castings Open
In the paper, we present results of stress analysis in domains which are a mixture of solid and liquid phases. Such mixtures occur in solidifying castings and are a result of forming a structure with solid skeleton and filling of a liquid …
Parallel-In-Space-Time, Adaptive Finite Element Framework for Nonlinear Parabolic Equations Open
We present an adaptive methodology for the solution of (linear and) non-linear time dependent problems that is especially tailored for massively parallel computations. The basic concept is to solve for large blocks of space-time unknowns i…
A computer simulation of solidification taking into account the movement of the liquid phase Open
In the paper, we present the results of solidification simulation taking into account the movement of the liquid phase. The results are obtained from an author software which is implemented on the base of a stabilized finite elements metho…
Engineering calculations for complex geometric domains Open
The paper aims to present the possibility of performing engineering calculations in domains of complex shapes expressed by mathematical descriptions. We focus on calculations done with the use of the Finite Element Method. An example of th…
Numerical Problems Related to Solving the Navier-Stokes Equations in Connection with the Heat Transfer with the Use of FEM Open
The paper presents a numerical solution to the unsteady form of the Navier-Stokes (N-S) equations along with the heat transfer equation. The problem of mass transfer with the energy transfer is very common in engineering, for instance, in …
Massively parallel-in-space-time, adaptive finite element framework for non-linear parabolic equations Open
We present an adaptive methodology for the solution of (linear and) non-linear time dependent problems that is especially tailored for massively parallel computations. The basic concept is to solve for large blocks of space-time unknowns i…
Numerical determination of equiaxed grain radii arising in the casting during 3D simulation of solidification Open
The knowledge of material structure allows to predict the mechanical properties of alloy casting. Such structure can be modelled in micro- and mesoscale. The first way is connected with alloy morphology and enables one to find out the shap…