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Isogeometric analysis (IGA) is a numerical method for solving partial differential equations (PDEs), which was introduced with the aim of integrating finite element analysis with computer-aided design systems. The main idea of the method is to use the same spline basis functions which describe the geometry in CAD systems for the approximation of solution fields in the finite element method (FEM). Originally, NURBS which is a standard technology employed in CAD systems was adopted as basis functions in IGA but there were several variants of IGA using other technologies such as T-splines, PHT splines, and subdivision surfaces as basis functions. In general, IGA offers two key advantages over classical FEM: (i) by describing the CAD geometry exactly using smooth, high-order spline functions, the mesh generation process is simplified and the interoperability between CAD and FEM is improved, (ii) IGA can be viewed as a high-order finite element method which offers basis functions with high inter-element continuity and therefore can provide a primal variational formulation of high-order PDEs in a straightforward fashion. The main goal of this thesis is to further advance isogeometric analysis by exploiting these major advantages, namely precise geometric modeling and the use of smooth high-order splines as basis functions, and develop robust computational methods for problems with complex geometry and/or complex multi-physics.
As the first contribution of this thesis, we leverage the precise geometric modeling of isogeometric analysis and propose a new method for its coupling with meshfree discretizations. We exploit the strengths of both methods by using IGA to provide a smooth, geometrically-exact surface discretization of the problem domain boundary, while the Reproducing Kernel Particle Method (RKPM) discretization is used to provide the volumetric discretization of the domain interior. The coupling strategy is based upon the higher-order consistency or reproducing conditions that are directly imposed in the physical domain. The resulting coupled method enjoys several favorable features: (i) it preserves the geometric exactness of IGA, (ii) it circumvents the need for global volumetric parameterization of the problem domain, (iii) it achieves arbitrary-order approximation accuracy while preserving higher-order smoothness of the discretization. Several numerical examples are solved to show the optimal convergence properties of the coupled IGA–RKPM formulation, and to demonstrate its effectiveness in constructing volumetric discretizations for complex-geometry objects.
As for the next contribution, we exploit the use of smooth, high-order spline basis functions in IGA to solve high-order surface PDEs governing the morphological evolution of vesicles. These governing equations are often consisted of geometric PDEs, high-order PDEs on stationary or evolving surfaces, or a combination of them. We propose an isogeometric formulation for solving these PDEs. In the context of geometric PDEs, we consider phase-field approximations of mean curvature flow and Willmore flow problems and numerically study the convergence behavior of isogeometric analysis for these problems. As a model problem for high-order PDEs on stationary surfaces, we consider the Cahn–Hilliard equation on a sphere, where the surface is modeled using a phase-field approach. As for the high-order PDEs on evolving surfaces, a phase-field model of a deforming multi-component vesicle, which consists of two fourth-order nonlinear PDEs, is solved using the isogeometric analysis in a primal variational framework. Through several numerical examples in 2D, 3D and axisymmetric 3D settings, we show the robustness of IGA for solving the considered phase-field models.
Finally, we present a monolithic, implicit formulation based on isogeometric analysis and generalized-alpha time integration for simulating hydrodynamics of vesicles according to a phase-field model. Compared to earlier works, the number of equations of the phase-field model which need to be solved is reduced by leveraging high continuity of NURBS functions, and the algorithm is extended to 3D settings. We use residual-based variational multi-scale method (RBVMS) for solving Navier–Stokes equations, while the rest of PDEs in the phase-field model are treated using a standard Galerkin-based IGA. We introduce the resistive immersed surface (RIS) method into the formulation which can be employed for an implicit description of complex geometries using a diffuse-interface approach. The implementation highlights the robustness of the RBVMS method for Navier–Stokes equations of incompressible flows with non-trivial localized forcing terms including bending and tension forces of the vesicle. The potential of the phase-field model and isogeometric analysis for accurate simulation of a variety of fluid-vesicle interaction problems in 2D and 3D is demonstrated.

Broadband dielectric measurement methods based on vector network analyzer coupled with coaxial transmission line cell (CC) and open-ended coaxial probe (OC) are simply reviewed, by which the dielectric behaviors in the frequency range of 1 MHz to 3 GHz of two practical geomaterials are investigated. Kaolin after modified compaction with different water contents is measured by using CC. The results are consistent with previous study on standardized compacted kaolin and suggest that the dielectric properties at frequencies below 100 MHz are not only a function of water content but also functions of other soil state parameters including dry density. The hydration process of a commercial grout is monitored in real time by using OC. It is found that the time dependent dielectric properties can accurately reveal the different stages of the hydration process. These measurement results demonstrate the practicability of the introduced methods in determining dielectric properties of soft geomaterials.

In recent years, substantial attention has been devoted to thermoelastic multifield problems and their numerical analysis. Thermoelasticity is one of the important categories of multifield problems which deals with the effect of mechanical and thermal disturbances on an elastic body. In other words, thermoelasticity encompasses the phenomena that describe the elastic and thermal behavior of solids and their interactions under thermo-mechanical loadings. Since providing an analytical solution for general coupled thermoelasticity problems is mathematically complicated, the development of alternative numerical solution techniques seems essential.
Due to the nature of numerical analysis methods, presence of error in results is inevitable, therefore in any numerical simulation, the main concern is the accuracy of the approximation. There are different error estimation (EE) methods to assess the overall quality of numerical approximation. In many real-life numerical simulations, not only the overall error, but also the local error or error in a particular quantity of interest is of main interest. The error estimation techniques which are developed to evaluate the error in the quantity of interest are known as “goal-oriented” error estimation (GOEE) methods.
This project, for the first time, investigates the classical a posteriori error estimation and goal-oriented a posteriori error estimation in 2D/3D thermoelasticity problems. Generally, the a posteriori error estimation techniques can be categorized into two major branches of recovery-based and residual-based error estimators. In this research, application of both recovery- and residual-based error estimators in thermoelasticity are studied. Moreover, in order to reduce the error in the quantity of interest efficiently and optimally in 2D and 3D thermoelastic problems, goal-oriented adaptive mesh refinement is performed.
As the first application category, the error estimation in classical Thermoelasticity (CTE) is investigated. In the first step, a rh-adaptive thermo-mechanical formulation based on goal-oriented error estimation is proposed.The developed goal-oriented error estimation relies on different stress recovery techniques, i.e., the superconvergent patch recovery (SPR), L2-projection patch recovery (L2-PR), and weighted superconvergent patch recovery (WSPR). Moreover, a new adaptive refinement strategy (ARS) is presented that minimizes the error in a quantity of interest and refines the discretization such that the error is equally distributed in the refined mesh. The method is validated by numerous numerical examples where an analytical solution or reference solution is available.
After investigating error estimation in classical thermoelasticity and evaluating the quality of presented error estimators, we extended the application of the developed goal-oriented error estimation and the associated adaptive refinement technique to the classical fully coupled dynamic thermoelasticity. In this part, we present an adaptive method for coupled dynamic thermoelasticity problems based on goal-oriented error estimation. We use dimensionless variables in the finite element formulation and for the time integration we employ the acceleration-based Newmark-_ method. In this part, the SPR, L2-PR, and WSPR recovery methods are exploited to estimate the error in the quantity of interest (QoI). By using
adaptive refinement in space, the error in the quantity of interest is minimized. Therefore, the discretization is refined such that the error is equally distributed in the refined mesh. We demonstrate the efficiency of this method by numerous numerical examples.
After studying the recovery-based error estimators, we investigated the residual-based error estimation in thermoelasticity. In the last part of this research, we present a 3D adaptive method for thermoelastic problems based on goal-oriented error estimation where the error is measured with respect to a pointwise quantity of interest. We developed a method for a posteriori error estimation and mesh adaptation based on dual weighted residual (DWR) method relying on the duality principles and consisting of an adjoint problem solution. Here, we consider the application of the derived estimator and mesh refinement to two-/three-dimensional (2D/3D) thermo-mechanical multifield problems. In this study, the goal is considered to be given by singular pointwise functions, such as the point value or point value derivative at a specific point of interest (PoI). An adaptive algorithm has been adopted to refine the mesh to minimize the goal in the quantity of interest.
The mesh adaptivity procedure based on the DWR method is performed by adaptive local h-refinement/coarsening with allowed hanging nodes. According to the proposed DWR method, the error contribution of each element is evaluated. In the refinement process, the contribution of each element to the goal error is considered as the mesh refinement criterion.
In this study, we substantiate the accuracy and performance of this method by several numerical examples with available analytical solutions. Here, 2D and 3D problems under thermo-mechanical loadings are considered as benchmark problems. To show how accurately the derived estimator captures the exact error in the evaluation of the pointwise quantity of interest, in all examples, considering the analytical solutions, the goal error effectivity index as a standard measure of the quality of an estimator is calculated. Moreover, in order to demonstrate the efficiency of the proposed method and show the optimal behavior of the employed refinement method, the results of different conventional error estimators and refinement techniques (e.g., global uniform refinement, Kelly, and weighted Kelly techniques) are used for comparison.

Image Analysis Using Human Body Geometry and Size Proportion Science for Action Classiﬁcation
(2020)

Gestures are one of the basic modes of human communication and are usually used to represent different actions. Automatic recognition of these actions forms the basis for solving more complex problems like human behavior analysis, video surveillance, event detection, and sign language recognition, etc. Action recognition from images is a challenging task as the key information like temporal data, object trajectory, and optical flow are not available in still images. While measuring the size of different regions of the human body i.e., step size, arms span, length of the arm, forearm, and hand, etc., provides valuable clues for identification of the human actions. In this article, a framework for classification of the human actions is presented where humans are detected and localized through faster region-convolutional neural networks followed by morphological image processing techniques. Furthermore, geometric features from human blob are extracted and incorporated into the classification rules for the six human actions i.e., standing, walking, single-hand side wave, single-hand top wave, both hands side wave, and both hands top wave. The performance of the proposed technique has been evaluated using precision, recall, omission error, and commission error. The proposed technique has been comparatively analyzed in terms of overall accuracy with existing approaches showing that it performs well in contrast to its counterparts.

Material properties play a critical role in durable products manufacturing. Estimation of the precise characteristics in different scales requires complex and expensive experimental measurements. Potentially, computational methods can provide a platform to determine the fundamental properties before the final experiment. Multi-scale computational modeling leads to the modeling of the various time, and length scales include nano, micro, meso, and macro scales. These scales can be modeled separately or in correlation with coarser scales. Depend on the interested scales modeling, the right selection of multi-scale methods leads to reliable results and affordable computational cost. The present dissertation deals with the problems in various length and time scales using computational methods include density functional theory (DFT), molecular mechanics (MM), molecular dynamics (MD), and finite element (FE) methods.
Physical and chemical interactions in lower scales determine the coarser scale properties. Particles interaction modeling and exploring fundamental properties are significant challenges of computational science. Downscale modelings need more computational effort due to a large number of interacted atoms/particles. To deal with this problem and bring up a fine-scale (nano) as a coarse-scale (macro) problem, we extended an atomic-continuum framework. The discrete atomic models solve as a continuum problem using the computationally efficient FE method. MM or force field method based on a set of assumptions approximates a solution on the atomic scale. In this method, atoms and bonds model as a harmonic oscillator with a system of mass and springs. The negative gradient of the potential energy equal to the forces on each atom. In this way, each bond's total potential energy includes bonded, and non-bonded energies are simulated as equivalent structural strain energies. Finally, the chemical nature of the atomic bond is modeled as a piezoelectric beam element that solves by the FE method.
Exploring novel materials with unique properties is a demand for various industrial applications. During the last decade, many two-dimensional (2D) materials have been synthesized and shown outstanding properties. Investigation of the probable defects during the formation/fabrication process and studying their strength under severe service life are the critical tasks to explore performance prospects. We studied various defects include nano crack, notch, and point vacancy (Stone-Wales defect) defects employing MD analysis. Classical MD has been used to simulate a considerable amount of molecules at micro-, and meso- scales. Pristine and defective nanosheet structures considered under the uniaxial tensile loading at various temperatures using open-source LAMMPS codes. The results were visualized with the open-source software of OVITO and VMD.
Quantum based first principle calculations have been conducting at electronic scales and known as the most accurate Ab initio methods. However, they are computationally expensive to apply for large systems. We used density functional theory (DFT) to estimate the mechanical and electrochemical response of the 2D materials. Many-body Schrödinger's equation describes the motion and interactions of the solid-state particles. Solid describes as a system of positive nuclei and negative electrons, all electromagnetically interacting with each other, where the wave function theory describes the quantum state of the set of particles. However, dealing with the 3N coordinates of the electrons, nuclei, and N coordinates of the electrons spin components makes the governing equation unsolvable for just a few interacted atoms. Some assumptions and theories like Born Oppenheimer and Hartree-Fock mean-field and Hohenberg-Kohn theories are needed to treat with this equation. First, Born Oppenheimer approximation reduces it to the only electronic coordinates. Then Kohn and Sham, based on Hartree-Fock and Hohenberg-Kohn theories, assumed an equivalent fictitious non-interacting electrons system as an electron density functional such that their ground state energies are equal to a set of interacting electrons. Exchange-correlation energy functionals are responsible for satisfying the equivalency between both systems. The exact form of the exchange-correlation functional is not known. However, there are widely used methods to derive functionals like local density approximation (LDA), Generalized gradient approximation (GGA), and hybrid functionals (e.g., B3LYP). In our study, DFT performed using VASP codes within the GGA/PBE approximation, and visualization/post-processing of the results realized via open-source software of VESTA.
The extensive DFT calculations are conducted 2D nanomaterials prospects as anode/cathode electrode materials for batteries. Metal-ion batteries' performance strongly depends on the design of novel electrode material. Two-dimensional (2D) materials have developed a remarkable interest in using as an electrode in battery cells due to their excellent properties. Desirable battery energy storage systems (BESS) must satisfy the high energy density, safe operation, and efficient production costs. Batteries have been using in electronic devices and provide a solution to the environmental issues and store the discontinuous energies generated from renewable wind or solar power plants. Therefore, exploring optimal electrode materials can improve storage capacity and charging/discharging rates, leading to the design of advanced batteries.
Our results in multiple scales highlight not only the proposed and employed methods' efficiencies but also promising prospect of recently synthesized nanomaterials and their applications as an anode material. In this way, first, a novel approach developed for the modeling of the 1D nanotube as a continuum piezoelectric beam element. The results converged and matched closely with those from experiments and other more complex models. Then mechanical properties of nanosheets estimated and the failure mechanisms results provide a useful guide for further use in prospect applications. Our results indicated a comprehensive and useful vision concerning the mechanical properties of nanosheets with/without defects. Finally, mechanical and electrochemical properties of the several 2D nanomaterials are explored for the first time—their application performance as an anode material illustrates high potentials in manufacturing super-stretchable and ultrahigh-capacity battery energy storage systems (BESS). Our results exhibited better performance in comparison to the available commercial anode materials.

The production of a desired product needs an effective use of the experimental model. The present study proposes an extreme learning machine (ELM) and a support vector machine (SVM) integrated with the response surface methodology (RSM) to solve the complexity in optimization and prediction of the ethyl ester and methyl ester production process. The novel hybrid models of ELM-RSM and ELM-SVM are further used as a case study to estimate the yield of methyl and ethyl esters through a trans-esterification process from waste cooking oil (WCO) based on American Society for Testing and Materials (ASTM) standards. The results of the prediction phase were also compared with artificial neural networks (ANNs) and adaptive neuro-fuzzy inference system (ANFIS), which were recently developed by the second author of this study. Based on the results, an ELM with a correlation coefficient of 0.9815 and 0.9863 for methyl and ethyl esters, respectively, had a high estimation capability compared with that for SVM, ANNs, and ANFIS. Accordingly, the maximum production yield was obtained in the case of using ELM-RSM of 96.86% for ethyl ester at a temperature of 68.48 °C, a catalyst value of 1.15 wt. %, mixing intensity of 650.07 rpm, and an alcohol to oil molar ratio (A/O) of 5.77; for methyl ester, the production yield was 98.46% at a temperature of 67.62 °C, a catalyst value of 1.1 wt. %, mixing intensity of 709.42 rpm, and an A/O of 6.09. Therefore, ELM-RSM increased the production yield by 3.6% for ethyl ester and 3.1% for methyl ester, compared with those for the experimental data.

We proposed two diﬀerent time-dependent modeling approaches for variation of device characteristics of perovskite solar cells under stress conditions. The first approach follows Sah-Noyce-Shockley (SNS) model based on Shockley–Read–Hall recombination/generation across the depletion width of pn junction and the second approach is based on thermionic emission model for Schottky diodes. The connecting point of these approaches to time variation is the time-dependent defect generation in depletion width (W) of the junction. We have fitted the two models with experimental data reported in the literature to perovskite solar cell and found out that each model has a superior explanation for degradation of device metrics e.g. current density and eﬃciency by time under stress conditions. Nevertheless, the Sah-Noyce-Shockley model is more reliable than thermionic emission at least for solar cells.

Water substantially affects nearly all physical, chemical and biological processes on the Earth. Recent Mars observations as well as laboratory investigations suggest that water is a key factor of current physical and chemical processes on the Martian surface, e.g. rheological phenomena. Therefore it is of particular interest to get information about the liquid-like state of water on Martian analogue soils for temperatures below 0 °C. To this end, a parallel plate capacitor has been developed to obtain isothermal dielectric spectra of fine-grained soils in the frequency range from 10 Hz to 1.1 MHz at Martian-like temperatures down to −70 °C. Two Martian analogue soils have been investigated: a Ca-bentonite (specific surface of 237 m2 g−1, up to 9.4% w / w gravimetric water content) and JSC Mars 1, a volcanic ash (specific surface of 146 m2 g−1, up to 7.4% w / w). Three soil-specific relaxation processes are observed in the investigated frequency–temperature range: two weak high-frequency processes (bound or hydrated water as well as ice) and a strong low-frequency process due to counter-ion relaxation and the Maxwell–Wagner effect. To characterize the dielectric relaxation behaviour, a generalized fractional dielectric relaxation model was applied assuming three active relaxation processes with relaxation time of the ith process modelled with an Eyring equation. The real part of effective complex soil permittivity at 350 kHz was used to determine ice and liquid-like water content by means of the Birchak or CRIM equation. There are evidence that bentonite down to −70 °C has a liquid-like water content of 1.17 monolayers and JSC Mars 1 a liquid-like water content of 1.96 monolayers.