Inverse unsteady heat conduction problem of second kind

The problem of determining the time-dependent heat flux imposed on the boundary of a solid slab from the temperature distribution at the final time is solved by the conjugate gradient (CG) and the truncated singular value decomposition (TSVD) methods. The Tikhonov regularization is used to regularize the solution when the given data contain random errors. The recovering of the exact boundary condition is shown to depend on the total time of the heating/cooling process. It is found that the exact boundary heat flux can be recovered for about one tenth of the diffusion time, beyond which we obtain only the time-averaged heat flux. However, by using a modified conjugate gradient method, we may reconstruct the boundary heat flux for much larger times if its initial value is known. We also show that these methods can be effectively used to solve the control problem

Simulation of time-dependent compressible viscous flows using central and upwind-biased finite-difference techniques

Four time-dependent numerical algorithms for the prediction of unsteady, viscous compressible flows are compared. The analyses are based on the time-dependent Navier-Stokes equations expressed in a generalized curvilinear coordinate system. The methods tested include three traditional central-difference algorithms, and a new upwind-biased algorithm utilizing an implicit, time-marching relaxation procedure based on Newton iteration. Aerodynamic predictions are compared for internal duct-type flows and cascaded turbomachinery flows with spatial periodicity. Two-dimensional internal duct-type flow predictions are performed using an H-type grid system. Planar cascade flows are analyzed using a numerically generated, capped, body-centered, O-type grid system. Initial results are presented for critical and supercritical steady inviscid flow about an isolated cylinder. These predictions are verified by comparisons with published computational results from a similar calculation. Results from each method are then further verified by comparison with experimental data for the more demanding case of flow through a two-dimensional turbine cascade. Inviscid predictions are presented for two different transonic turbine cascade flows. All of the codes demonstrate good agreement for steady viscous flow about a high-turning turbine vane with a leading edge separation. The viscous flow results show a marked improvement over the inviscid results in the region near the separation bubble. Viscous flow results are then further verified in finer detail through comparison with the similarity solution for a flat plate boundary-layer flow. The usefulness of the schemes for the prediction of unsteady flows is demonstrated by examining the unsteady viscous flow resulting from a sinusoidally oscillating flat plate in the vicinity of a stagnant fluid. Predicted results are compared with the analytical solution for this flow. Finally, numerical results are compared with flow visualization and experimental data for the unsteady flow resulting from an impulsively started cylinder. Each algorithm demonstrates unique qualities which may be interpreted as either advantageous or disadvantageous, making it difficult to select an optimum scheme. The preferred method is perhaps best chosen based on the experience of the user and the particular application

A Spectral Iterative Approach for Analyzing the Scattering of Cylindrical Waves from One Dimensional Wire Gratings

The scattering of cylindrical waves, infinite in the axial direction, from a one dimensional infinite, planar, periodic array of wires is investigated. The cylindrical wavefront is divided into planar segments. Each planar segment is treated individually as an infinite plane wave incident upon the periodic structure. The reflection characteristics of each plane wave is determined by analyzing the electromagnetic scattered fields using the secant method to solve an iterative algorithm. The derivation of the method as applied to surfaces containing a one dimensional parallel thin wire grating is presented. The reflection coefficients for cylindrical waves are determined by combining the reflection coefficients of the planar segments. The reflection characteristics of the grating as a function of wire spacing, wire thickness and polarization of the incident field are calculated

Analysis of Frequency Selective Surfaces with Ferrite Substrates

Frequency selective surfaces (FSS) have numerous applications in several microwave and optical systems. Most frequency selective surface structures have one or more dielectric substrates. In this work, instead of traditional dielectric substrates, ferrite substrates are used under different dc bias conditions. By using ferrite materials, one can change the spectral properties of these structures without physically altering them. An applied magnetic field (dc bias) on the ferrite substrate changes its properties and hence the electrical dimensions of the elements comprising the periodic structure. Thus by simply applying a dc bias, the transmission and reflection properties of the periodic structure can be changed. That leads to a tuning mechanism which allows the designer, by varying the externally applied dc magnetic field, to obtain a more desirable frequency response. In this work, the transmission matrices for the ferrite substrate and the air, above and below the ferrite substrate are derived. By combining these transmission matrices along with the boundary conditions, the spectral domain Green\u27s function is obtained. This process is carried out for both the in-plane bias and perpendicular bias of the ferrite. The induced current on the conductor patch is solved by the method of moments in the spectral domain. Roof toping functions are used as both expansion and test functions. Several results are presented to show the tunability of frequency selective surfaces with ferrite substrates as a function of the applied dc bias. Other unique characteristics of the frequency selective surfaces on ferrite substrates are also presented and discussed. The design procedure for frequency selective surfaces by neural network algorithms is introduced

International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book

The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions. This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more

Rapid 3D Phase Contrast Magnetic Resonance Angiography through High-Moment Velocity Encoding and 3D Parallel Imaging

abstract: Phase contrast magnetic resonance angiography (PCMRA) is a non-invasive imaging modality that is capable of producing quantitative vascular flow velocity information. The encoding of velocity information can significantly increase the imaging acquisition and reconstruction durations associated with this technique. The purpose of this work is to provide mechanisms for reducing the scan time of a 3D phase contrast exam, so that hemodynamic velocity data may be acquired robustly and with a high sensitivity. The methods developed in this work focus on the reduction of scan duration and reconstruction computation of a neurovascular PCMRA exam. The reductions in scan duration are made through a combination of advances in imaging and velocity encoding methods. The imaging improvements are explored using rapid 3D imaging techniques such as spiral projection imaging (SPI), Fermat looped orthogonally encoded trajectories (FLORET), stack of spirals and stack of cones trajectories. Scan durations are also shortened through the use and development of a novel parallel imaging technique called Pretty Easy Parallel Imaging (PEPI). Improvements in the computational efficiency of PEPI and in general MRI reconstruction are made in the area of sample density estimation and correction of 3D trajectories. A new method of velocity encoding is demonstrated to provide more efficient signal to noise ratio (SNR) gains than current state of the art methods. The proposed velocity encoding achieves improved SNR through the use of high gradient moments and by resolving phase aliasing through the use measurement geometry and non-linear constraints.Dissertation/ThesisPh.D. Bioengineering 201