The Guyer–Krumhansl heat conduction model has emerged as a thermodynamically consistent linearized continuum framework for describing rapid thermal transport in heterogeneous and layered materials, porous media, and low-temperature regimes where classical Fourier law fails to capture experimentally observed phenomena. Despite its clear physical relevance, the reliable numerical solution of the associated initial–boundary value problems remains challenging. Standard mesh-refinement-based (h-version) finite element methods may suffer from poor convergence behavior, spurious oscillations, or loss of accuracy, particularly in parameter regimes corresponding to over-diffusive behavior or strong interfacial effects. These limitations make it necessary to construct more robust and higher-order numerical strategies equipped with much more flexible refinement schemes.In this work, a two-field radial basis function finite difference method based on odd order polyharmonic spline augmented with monomials is developed for the space discretization of the Guyer–Krumhansl model in layered media with Kapitza-type imperfect thermal interface conditions, using the implicit scheme for the time discretization. Both uniform and Halton-type quasi-random space point distributions are employed to investigate the h-convergence behavior of temperature response functions at discrete space points. Particular attention is devoted to the influence of the monomial degree p, the non-classical material parameters such as κ2 and τ, and the thermal resistance R on convergence order and accuracy. The results demonstrate uniformly stable algebraic convergences consistent with theoretical predictions. Increasing the monomial degree p improves the convergence rate, while the thermal resistance does not affect the order of convergence.

In this paper, new multi-field variational formulations are derived for solving the following thermodynamic models: (i) ballistic-conductive system, (ii) the Guyer-Krumhansl heat conduction model and (iii) the Maxwell-Cattaneo-Vernotte model as some models of the extended irreversible thermodynamic, handling the temperature, the heat flux and the current density of heat flux as independent field variables. Based on these variational approaches as mathematical background, a family of mixed hp-version finite element methods, which is capable of reliably and efficiently modeling the temperature responses, is designed. The solutions provided by the constructed hp-FE framework are illustrated for the following two heat pulse experiments as benchmark problems: (1) sinusoid laser pulse heating process and (2) rectangular (step-like) laser pulse train. It is shown that stable, oscillation-free temperature response functions can be obtained not only for the ballistic-conductive system and the Maxwell-Cattaneo-Vernotte model but also for the under-diffuse and the over-diffuse parameter settings of the Guyer-Krumhansl heat conduction model.

Modern manufacturing technologies allow heterogeneous materials with complex inner structures (e.g., foams) to be easily produced. However, their utilization is not straightforward, as the classical constitutive laws are not necessarily valid. According to various experimental observations, the Guyer–Krumhansl equation is a promising candidate for modeling such complex structures. However, practical applications need a reliable and efficient algorithm capable of handling both complex geometries and advanced heat equations. In the present paper, we derive new two-field variational formulations which treat the temperature and the heat flux as independent field variables, and we develop new, advanced hp-type mixed finite element methods, which can be reliably applied. We investigate their convergence properties for various situations, challenging in relation to stability and the treatment of fast propagation speeds. That algorithm is also proved to be outstandingly efficient, providing solutions four magnitudes faster than commercial algorithms.

On the basis of numerous experimental studies the Guyer-Krumhansl heat conductivity model can be considered as one of the most promising theoretical models to simulate the low temperature processes and the thermal behavior of such complex structures as materials with inhomogeneities and interfaces, as well as porous materials. However, the classical h-version finite element methods do not provide convergent and accurate results for the solution of the Guyer-Krumhansl heat conductivity model. In recent paper, a new three-field variational formulation is derived treating the temperature, the heat flow and its current density as independent variables. Both the temperature-and the heat flow boundary condition are weakly imposed, i.e., built in the variational form. Based on this variational background, a new, hp-version mixed finite element method is constructed. The h-and p-convergence behaviors of the temperature and the heat flow are analyzed on the transient region for two representative model problems: (i) a rapid heating process with exponentially changing rate and (ii) a ramp -type heating process. The relative and absolute errors are measured in maximum norm. From the computational experiments it follows that the mixed hp-finite element method gives reliable, robust (uniformly stable) results not only for the h-but also for the p-approximation in the case of both the temperature and the heat flow.

Three-dimensional printing is a promising technology that offers increased freedom to create topologically optimised electrical machine designs with a much smaller layer thickness achievable with the current, laminated steel-sheet-based technology. These composite materials have promising magnetic behaviour, which can be competitive with the current magnetic materials. Accurately calculating the iron losses is challenging due to magnetic steels’ highly nonlinear hysteretic behaviour. Many numerical methodologies have been developed and applied in FEM-based simulations from the first introduced Steinmetz formulae. However, these old curve-fitting-based iron loss models are still actively used in modern finite-element solvers due to their simplicity and high computational demand for more-accurate mathematical methods, such as Preisach- or Jiles–Atherton-model-based calculations. In the case of 3D-printed electrical machines, where the printed material can have a strongly anisotropic behaviour and it is hard to define a standardised measurement, the applicability of the curve-fitting-based iron loss methodologies is limited. The following paper proposes an overview of the current problems and solutions for iron loss calculation and measurement methodologies and discusses their applicability in designing and optimising 3D-printed electrical machines.

Many image-based recognition tasks are highly susceptible to different types of natural phenomena like foggy weather, snow, or rain. The participating media will likely obscure important details necessary for these algorithms to work correctly. Still, these aspects could be recovered in certain situations with prior information about the underlying light interactions. This could be done with certain heuristics or with the nowadays popular deep-learning based methods. In this paper, we review and compare the results of two approaches to remove or scale down the effects of foggy weather. We also examine how these results can be applied to high resolution satellite images of land surfaces.

Ambient occlusion is a popular method to enhance the visuals of real-time applications. The generally accepted equation assumes that incoming ambient lighting is uniform in the enclosing hemisphere around the surface point. This assumption does not always hold and can cause artifacts. With screen-space techniques the artifact may not be present, because of the lack of information, but it becomes visible with more accurate methods. This is especially true for ray tracing based implementations which are widely used to create the ground truth image to measure other techniques. With recent advancements of the graphics hardware, they also found their way into real-time applications where these shortcomings were neither discussed nor addressed. In this paper we analyze the problem and demonstrate its presence in popular game engines. We also propose a ray tracing based extension to eliminate these artifact in a physically plausible way.

In this research work, the radial basis function finite difference method (RBF-FD) is further developed to solve one- and two-dimensional boundary value problems in linear elasticity. The related differentiation weights are generated by using the extended version of the RBF utilizing a polynomial basis. The type of the RBF is restricted to polyharmonic splines (PHS), i.e., a combination of the odd m -order PHS ϕ (r)=r^m with additional polynomials up to degree p will serve as the basis. Furthermore, a new residual-based adaptive point-cloud refinement algorithm will be presented and its numerical performance will be demonstrated. The computational efficiency of the PHS RBF-FD approach is tested by means of the relative errors measured in ℓ _2 -norm on several representative benchmark problems with smooth and non-smooth solutions, using h -adaptive, uniform, and quasi-uniform point-cloud refinement.

Dynamic tomography reconstructs a time activity curve (TAC) for every voxel assuming that the algebraic form of the function is known a priori. The algebraic form derived from the analysis of compartmental models depends nonlinearly on the nonnegative parameters to be determined. Direct methods apply fitting in every iteration step. Because of the iterative nature of the maximum likelihood–expectation maximization (ML–EM) reconstruction, the fitting result of the previous step can serve as a good starting point in the current step; thus, after the first iteration we have a guess that is not far from the solution, which allows the use of gradient-based local optimization methods. However, finding good initial guesses for the first ML–EM iteration is a critical problem since gradient-based local optimization algorithms do not guarantee convergence to the global optimum if they are started at an inappropriate location. This paper examines the robust solution of the fitting problem both in the initial phase and during the ML–EM iteration. This solution is implemented on GPUs and is built into the 4D reconstruction module of the TeraTomo software.

The paper presents a comparative analysis of different commercial and academic software. The comparison aims to examine how the integrated adaptive grid refinement methodologies can deal with challenging, electromagnetic-field related problems. For this comparison, two benchmark problems were examined in the paper. The first example is a solution of an L-shape domain like test problem, which has a singularity at a certain point in the geometry. The second problem is an induction heated aluminum rod, which accurate solution needs to solve a non-linear, coupled physical fields. The accurate solution of this problem requires applying adaptive mesh generation strategies or applying a very fine mesh in the electromagnetic domain, which can significantly increase the computational complexity. The results show that the fully-hp adaptive meshing strategies, which are integrated into Agros-suite, can significantly reduce the task's computational complexity compared to the automatic h-adaptivity, which is part of the examined, popular commercial solvers.

A newly-developed, dimensionally reduced, hp-type axisymmetric shell finite element model is extended to linear elastodynamic problems of thin shells of revolution. The hp shell finite element relies on the hybridized version of a three-field dual-mixed variational formulation, the application of which dictates the obligate usage of the inverse threedimensional constitutive relation for homogeneous and isotropic materials, thereby ensuring the volumetric locking-free characteristic of the shell model at theory level. The fundamental fields are the a priori non-symmetric stress tensor, the displacement vector, the infinitesimal rotation vector and the hybrid variable defined on the element interfaces. Since the dimensional reduction process guided by this hybrid-mixed formulation does not necessitate the use of any classical kinematic assumptions appearing in the scientific literature, the inverse 3D Hooke's law does not have to be modified. The numerical performance of the shell finite element is analyzed comprehensively for natural frequency computations of clamped-free and simply supported, silicone, conoid, spherical and hyperboloid shells of revolution. From their relative error convergence behaviors it follows that the extended hybrid-mixed shell finite element is not sensitive to the decrease of the slenderness ratio, namely providing reliable, uniformly stable numerical results for both h and p-approximation. From theoretical point of view, the beneficial properties of the hybrid-mixed hp shell finite element model are as follows: (i) this is effectively applicable to modeling not only extremely thin but also moderately thick shell structures with transverse shear deformations, as well as (ii) both the through-the-thickness variation and the membrane stress normal to the shell mid-surface are retained as independent variables, making it much easier to upbuild shell model for contact problems. From numerical point of view, the nice feature of the hybrid-mixed hp shell finite element is that the global flexibility matrix of the system can be inverted block-wise at element level at cheap computational cost during the assembling procedure because of the hybridization technique. (c) 2021 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )

Depth of Interaction (DOI) PET scanners extend the data stored about photon detection events by the depth of the gamma photon's absorption in the detector crystals. Popular DOI-based reconstruction methods disregard photon scattering in the detectors and simply modify the endpoints of the Lines of Responses (LORs). However, such simplification reduces the accuracy of the resulting image. This paper proposes the incorporation of the modeling of inter-crystal scattering into DOI-based PET reconstructions. The transfer probabilities caused by inter-crystal scattering are determined off-line with Monte Carlo simulation and are built into the system matrix as a factored component.

We propose a novel method for multisample anti-aliasing in deferred shading. Our technique successfully reduces memory and bandwidth usage. The new model uses per-pixel linked lists to store the samples. We also introduce algorithms to construct the new G-Buffer in the geometry pass and to calculate the shading in the lighting pass. The algorithms are designed to enable further optimizations, similar to variable rate shading. We also propose methods to satisfy constraints of memory usage and processing time. We integrated the new method into a Vulkan based renderer. CCS Concepts • Computing methodologies → Rasterization; Antialiasing;

A new, general hp-version axisymmetric finite element is derived for the boundary value problems of thin linearly elastic shells of revolution, applying a complementary strain energy-based three-field dual-mixed variational principle. For the interpolation of the mid-surface geometry, non-uniform rational B-splines—NURBS—is used. The independent field variables of the weak formulation are the a priori non-symmetric stress tensor, the displacement vector, and the infinitesimal skew-symmetric rotation tensor. The theoretical model of the shell formulation is based on a consistent dimensional reduction process and a systematic variable-number reduction procedure. The inverse of the unvaried three-dimensional constitutive equation is employed since neither the classical kinematical assumptions nor the stress hypotheses are built in the mathematical model; namely, both the through-the-thickness variation and the normal stress to the shell mid-surface are not excluded. The new hp axisymmetric shell finite element is tested by a representative model problem for extremely thin and moderately thick, singly and doubly curved shells of negative and positive Gaussian curvature. Following from the numerical experiments, the constructed hp-shell finite element gives locking-free results not only for the displacement but also for the stresses.

A locking-free hp-version finite element is presented for linear elasticity problems of thin shells of revolution. The constructed hp-finite element is based on a hybridized dual-mixed variational formulation. The related theoretical model does not rely on the standard hypotheses used in the Naghdi- and Koiter shell theories, thus the unmodified three-dimensional constitutive equation can be applied. Nevertheless, since employing its inverse form, the hp-shell finite element is incompressibility locking free. Besides, neither the thickness variation nor the membrane stress normal to the shell mid-surface is not eliminated from the shell formulation, thus it can be extended to much complicated (contact) problems of more complex (composite), extremely thin and moderately thick shell structures. The new hp shell finite element is tested through some representative mixed and pure boundary value problems, namely bending- and membrane dominated situations, for singly and doubly curved shells of negative and positive Gaussian curvature. From the convergence behavior of the relative errors it follows that the developed hp-version shell finite element is insensitive to the decrease of the thickness value, i.e., membrane and shear locking-free, providing excellent numerical results not only for the displacement but also for the stresses computations. (C) 2019 Elsevier Ltd. All rights reserved.

In this paper we introduce a virtual reality room setup using commonly available, moderately expensive devices. We implement head position tracking with a Microsoft Kinect V2 sensor, and use an Android device with gyroscope to track user head rotation and to display the virtual world. Our workstation which handles the Kinect can also insert the point cloud of the user in the virtual world and can inspect its interaction in real time.

Dynamic Positron Emission Tomography (PET) reconstructs the space-time concentration function of a radiotracer by observing the detector hits of gamma-photon pairs born during the radiotracer decay. The computation is based on the maximum likelihood principle, i.e. we look for the space-time function that maximizes the probability of the actual measurements. The number of finite elements representing the spatio-temporal concentration and the number of events detected by the tomograph may be higher than a billion, thus the reconstruction requires supercomputer performance. The enormous computational burden can be handled by graphics processors (GPU) if the algorithm is decomposed to parallel, independent threads, and the storage requirements are kept under control. This paper proposes a scalable dynamic reconstruction system where the algorithm is decomposed to phases where each phase is efficiently mapped onto the massively parallel architecture of the GPU.

Tomography reconstruction is ill posed, thus regularization is needed to avoid overfitting. Total variation regularization modifies the maximum-likelihood objective by penalizing high variation solutions. The strength of regularization, called the regularization parameter, is usually set manually, because there is no straightforward method to find its optimal value. If the regularization parameter is too small, the reconstruction will be noisy. If it is too strong, the true signal is compromised and painted like or checkerboard pattern artifacts may show up. This paper proposes the application of deep learning techniques to control the regularization parameters dynamically during the reconstruction process. That is, the regularization parameter is automatically set and is modified in each iteration cycle to improve convergence. Unlike other techniques, we replace none of the components of the reconstruction algorithm by a trained neural network, but control the parameter of the TV-regularized ML-EM algorithm. Thus, reasonably sized training set can also lead to robust and efficient solutions. The algorithm is demonstrated for a 2D test scenario.

Some new dual and mixed variational formulations based on a priori nonsymmetric stresses will be developed for linearly coupled irreversible thermoelastodynamic problems associated with second sound effect according to the Lord–Shulman theory. Having introduced the entropy flux vector instead of the entropy field and defining the dissipation and the relaxation potential as the function of the entropy flux, a seven-field dual and mixed variational formulation will be derived from the complementary Biot–Hamilton-type variational principle, using the Lagrange multiplier method. The momentum-, the displacement- and the infinitesimal rotation vector, and the a priori nonsymmetric stress tensor, the temperature change, the entropy field and its flux vector are considered as the independent field variables of this formulation. In order to handle appropriately the six different groups of temporal prescriptions in the relaxed- and/or the strong form, two variational integrals will be incorporated into the seven-field functional. Then, eliminating the entropy from this formulation through the strong fulfillment of the constitutive relation for the temperature change with the use of the Legendre transformation between the enthalpy and Gibbs potential, a six-field dual and mixed action functional is obtained. As a further development, the elimination of the momentum- and the velocity vector from the six-field principle through the a priori satisfaction of the kinematic equation and the constitutive relation for the momentum vector leads to a five-field variational formulation. These principles are suitable for the transient analyses of the structures exposed to a thermal shock of short temporal domain or a large heat flux.

A three-dimensional weakly compressible Smoothed Particle Hydrodynamics (SPH) solver is presented and applied to simulate free-surface solitary waves generated in a quasi two-dimensional dam-break experiment. Test cases are constructed based on the measurement layouts of a dam-break experiment. The simulated wave propagation speeds are compared to the exact solutions of the Korteweg-de Vries (KdV) equation as a first order theory, and to a second order iterative approximation investigated in the literature. Free surface shapes of different simulation cases are investigated as well. The results show good agreement with the free surface shapes of the KdV equation as well as with the second order approximation of solitary wave propagation speeds.