A face-smoothed cell method for static and dynamic piezoelectric coupled problems on polyhedral meshes

Low-order discretization schemes are suitable for modeling 3-D multiphysics problems since a huge number of degrees of freedom (DoFs) is typically required by standard high-order Finite Element Method (FEM). On the other hand, polyhedral meshes ensure a great flexibility in the domain discretization and are thus suitable for complex model geometries. These features are useful for the multiphysics simulation of micro piezoelectric devices with a thin multi-layered and multi-material structure. The Cell Method (CM) is a low-order discretization scheme which has been mainly adopted up to now for electromagnetic problems but has not yet been used for mechanical problems with polyhedral discretization. This work extends the CM to piezo-elasticity by reformulating local constitutive relationships in terms of displacement gradient. In such a way, piecewise uniform edge basis functions defined on arbitrary polyhedral meshes can be used for discretizing local constitutive relationships. With the CM matrix assembly is completely Jacobian-free and do not require Gaussian integration, reducing code complexity. The smoothing technique, firstly introduced for FEM, is here extended to CM in order to avoid shear locking arising when low-order discretization is used for thin cantilevered beams under bending. The smoothed CM is validated for static and dynamic problems on a real test case by comparison with both second-order FEM and experimental data. Numerical results show that accuracy is retained even if a much lower number of DoFs is required compared to FEM

A high-performance boundary element method and its applications in engineering

As a semi-numerical and semi-analytical method, owing to the inherent advantage, of boundary-only discretisation, the boundary element method (BEM) has been widely applied to problems with complicated geometries, stress concentration problems, infinite domain problems, and many others. However, domain integrals and non-symmetrical and dense matrix systems are two obstacles for BEM which have hindered the its further development and application. This thesis is aimed at proposing a high-performance BEM to tackle the above two drawbacks and broaden the application scope of BEM. In this thesis, a detailed introduction to the traditional BEM is given and several popular algorithms are introduced or proposed to enhance the performance of BEM. Numerical examples in heat conduction analysis, thermoelastic analysis and thermoelastic fracture problems are performed to assess the efficiency and correction of the algorithms. In addition, necessary theoretical derivations are embraced for establishing novel boundary integral equations (BIEs) for specific engineering problems. The following three parts are the main content of this thesis. (1) The first part (Part II consisting of two chapters) is aimed at heat conduction analysis by BEM. The coefficient matrix of equations formed by BEM in solving problems is fully-populated which occupy large computer memory. To deal with that, the fast multipole method (FMM) is introduced to energize the line integration boundary element method (LIBEM) to performs better in efficiency. In addition, to compute domain integrals with known or unknown integrand functions which are caused by heat sources or heterogeneity, a novel BEM, the adaptive orthogonal interpolation moving least squares (AOIMLS) method enhanced LIBEM, which also inherits the advantage of boundary-only discretisation, is proposed. Unlike LIBEM, which is an accurate and stable method for computing domain integrals, but only works when the mathematical expression of integral function in domain integrals is known, the AOIMLS enhanced LIBEM can compute domain integrals with known or unknown integral functions, which ensures all the nonlinear and nonhomogeneous problems can be solved without domain discretisation. In addition, the AOIMLS can adaptively avoid singular or ill-conditioned moment matrices, thus ensuring the stability of the calculation results. (2) In the second part (Part III consisting of four chapters), the thermoelastic problems and fracture problems are the main objectives. Due to considering thermal loads, domain integrals appear in the BIEs of the thermoelastic problems, and the expression of integrand functions is known or not depending on the temperature distribution given or not, the AOIMLS enhanced LIBEM is introduced to conduct thermoelasticity analysis thereby. Besides, a series of novel unified boundary integral equations based on BEM and DDM are derived for solving fracture problems and thermoelastic fracture problems in finite and infinite domains. Two sets of unified BIEs are derived for fracture problems in finite and infinite domains based on the direct BEM and DDM respectively, which can provide accurate and stable results. Another two sets of BIEs are addressed by employing indirect BEM and DDM, which cannot ensure a stable result, thereby a modified indirect BEM is proposed which performs much more stable. Moreover, a set of novel BIEs based on the direct BEM and DDM for cracked domains under thermal stress is proposed. (3) In the third part (Part IV consisting of one chapter), a high-efficiency combined BEM and discrete element method (DEM) is proposed to compute the inner stress distribution and particle breakage of particle assemblies based on the solution mapping scheme. For the stress field computation of particles with similar geometry, a template particle is used as the representative particle, so that only the related coefficient matrices of one template particle in the local coordinate system are needed to be calculated, while the coefficient matrices of the other particles, can be obtained by mapping between the local and global coordinate systems. Thus, the combined BEM and DEM is much more effective when modelling a large-scale particle system with a small number of distinct possible particle shapes. Furthermore, with the help of the Hoek-Brown criterion, the possible cracks or breakage paths of a particle can be obtained

Advanced numerical modeling of semiconductor material properties and their device performances

With the renewed concept of "Materials by Design" attracting particular attentions from the engineering communities in recent years, numerical methods that can reliably predict the optical and electrical properties of materials is highly preferable. Since the growth or the synthesis of a "designed" material and the ensuing devices is usually prohibitively expensive and time-consuming, numerical simulation tools that predict the properties of a proposed material together with its device performance before production is especially important and cost-effective. Furthermore, as the technology advances, semiconductor devices have been pushed to operate at their material limits, which requires a thorough understanding of the materials' microscopic processes under different conditions. Therefore, developing numerical models that are capable of investigating the semiconductor properties from material level to device level is highly desirable. This dissertation develops a suite of numerical models in which optical absorption and Auger recombination in semiconductor materials are studied and simulated together with their device performances. In particular, Green's function theory with full band structures is employed to investigate the material properties by evaluating the broadening of the electronic bands under the perturbation of phonons. As a result, both direct and phonon-assisted indirect processes are computed and compared among different materials. Drift-diffusion model and a 3D Monte-Carlo model are subsequently used to simulate the device characteristics with the obtained material parameters. This work first determines the full band structures for Si, Ge, α-Sn, HgCdTe, InAsSb and InGaAs alloys from EPM model, and then investigated the materials' minority carrier lifetime for IR detector applications. Finally device level simulations using drift-diffusion and 3D Monte-Carlo models are demonstrated. In particular, two issues of developing 3D Monte-Carlo device simulation models, namely the use of unstructured spatial meshes and elimination of particle-mesh forces, are discussed, which are crucial in simulating modern semiconductor devices having complex geometry and doping profiles