Robust Preconditioned Iterative Solution Methods for Large-scale Nonsymmetric Problems

We study robust, preconditioned, iterative solution methods for largescale linear systems of equations, arising from different applications in geophysics and geotechnics. The first type of linear systems studied here, which are dense, arise from a boundary element type of discretization of crack propagation in brittle material. Numerical experiment show that simple algebraic preconditioning strategies results in iterative schemes that are highly competitive with a direct solution method. The second type of algebraic systems are nonsymmetric and indefinite and arise from finite element discretization of the partial differential equations describing the elastic part of glacial rebound processes. An equal order finite element discretization is analyzed and an optimal stabilization parameter is derived. The indefinite algebraic systems are of 2-by-2-block form, and therefore block preconditioners of block-factorized or block-triangular form ar

Harmonic Mitigation in Traction Drives

In railway traffic the low friction between wheel and rail causes long braking distances, normally much longer than the sight distance of the driver, i.e. if the driver starts the braking when a problem on the track is discovered, it might be too late to brake the train. Therefore, safe railway traffic can not only rely on the driver. It is necessary to have a signalling or even an automatic surveyor system, especially in densely populated areas, which supervises the positions of different trains along the track and organises the traffic. Such a system uses train detection systems to control whether a certain section of the track is occupied or not. Train detection systems can unfortunately be disturbed by harmonics, generated by the drive system of a rail vehicle. To reduce the risk of disturbance, the choice of modulation strategy and the use of line filters are critical tasks. In the design stage of the filter, it is necessary to be able to predict the generation of harmonics. This work presents fast algorithms for calculation of harmonics, generated by a traction drive system. The traction drive system, here described, is based on three phase induction motors, fed from voltage source machine and line converters. Non-ideal commutations are taken into account, which is urgent as these will generate undesirable low frequency harmonics. It is possible to compensate the effects of the non-ideal commutations, and in this work following compensation methods are investigated: - Dead time compensation, where the differential between the integral of the inverter output voltage, or rather the output flux, and the voltage time area reference, is fed back to the control system. - Position asymmetry compensation, in which the DC-component in the machine converter phase currents is fed back to the control system. - Compensation of a remaining DC-bias in Hall-effect current transducers. In the method, the fundamental component in the DC-link current is fed back to the control system. The compensation methods are found to effectively reduce the low frequencies. Thus the weight of the filters onboard the trains can be minimised, which considerably saves energy and costs of components

Robust Preconditioners Based on the Finite Element Framework

Robust preconditioners on block-triangular and block-factorized form for three types of linear systems of two-by-two block form are studied in this thesis. The first type of linear systems, which are dense, arise from a boundary element type of discretization of crack propagation problems. Numerical experiment show that simple algebraic preconditioning strategies results in iterative schemes that are highly competitive with a direct solution method. The second type of algebraic systems, which are sparse, indefinite and nonsymmetric, arise from a finite element (FE) discretization of the partial differential equations (PDE) that describe (visco)elastic glacial isostatic adjustment (GIA). The Schur complement approximation in the block preconditioners is constructed by assembly of local, exactly computed Schur matrices. The quality of the approximation is verified in numerical experiments. When the block preconditioners for the indefinite problem are combined with an inner iterative scheme preconditioned by a (nearly) optimal multilevel preconditioner, the resulting preconditioner is (nearly) optimal and robust with respect to problem size, material parameters, number of space dimensions, and coefficient jumps. Two approaches to mathematically formulate the PDEs for GIA are compared. In the first approach the equations are formulated in their full complexity, whereas in the second their formulation is confined to the features and restrictions of the employed FE package. Different solution methods for the algebraic problem are used in the two approaches. Analysis and numerical experiments reveal that the first strategy is more accurate and efficient than the latter. The block structure in the third type of algebraic systems is due to a fine-coarse splitting of the unknowns. The inverse of the pivot block is approximated by a sparse matrix which is assembled from local, exactly inverted matrices. Numerical experiments and analysis of the approximation show that it is robust with respect to problem size and coefficient jumps

Robust Preconditioners Based on the Finite Element Framework

Robust preconditioners on block-triangular and block-factorized form for three types of linear systems of two-by-two block form are studied in this thesis. The first type of linear systems, which are dense, arise from a boundary element type of discretization of crack propagation problems. Numerical experiment show that simple algebraic preconditioning strategies results in iterative schemes that are highly competitive with a direct solution method. The second type of algebraic systems, which are sparse, indefinite and nonsymmetric, arise from a finite element (FE) discretization of the partial differential equations (PDE) that describe (visco)elastic glacial isostatic adjustment (GIA). The Schur complement approximation in the block preconditioners is constructed by assembly of local, exactly computed Schur matrices. The quality of the approximation is verified in numerical experiments. When the block preconditioners for the indefinite problem are combined with an inner iterative scheme preconditioned by a (nearly) optimal multilevel preconditioner, the resulting preconditioner is (nearly) optimal and robust with respect to problem size, material parameters, number of space dimensions, and coefficient jumps. Two approaches to mathematically formulate the PDEs for GIA are compared. In the first approach the equations are formulated in their full complexity, whereas in the second their formulation is confined to the features and restrictions of the employed FE package. Different solution methods for the algebraic problem are used in the two approaches. Analysis and numerical experiments reveal that the first strategy is more accurate and efficient than the latter. The block structure in the third type of algebraic systems is due to a fine-coarse splitting of the unknowns. The inverse of the pivot block is approximated by a sparse matrix which is assembled from local, exactly inverted matrices. Numerical experiments and analysis of the approximation show that it is robust with respect to problem size and coefficient jumps

Robust Preconditioners Based on the Finite Element Framework

Robust preconditioners on block-triangular and block-factorized form for three types of linear systems of two-by-two block form are studied in this thesis. The first type of linear systems, which are dense, arise from a boundary element type of discretization of crack propagation problems. Numerical experiment show that simple algebraic preconditioning strategies results in iterative schemes that are highly competitive with a direct solution method. The second type of algebraic systems, which are sparse, indefinite and nonsymmetric, arise from a finite element (FE) discretization of the partial differential equations (PDE) that describe (visco)elastic glacial isostatic adjustment (GIA). The Schur complement approximation in the block preconditioners is constructed by assembly of local, exactly computed Schur matrices. The quality of the approximation is verified in numerical experiments. When the block preconditioners for the indefinite problem are combined with an inner iterative scheme preconditioned by a (nearly) optimal multilevel preconditioner, the resulting preconditioner is (nearly) optimal and robust with respect to problem size, material parameters, number of space dimensions, and coefficient jumps. Two approaches to mathematically formulate the PDEs for GIA are compared. In the first approach the equations are formulated in their full complexity, whereas in the second their formulation is confined to the features and restrictions of the employed FE package. Different solution methods for the algebraic problem are used in the two approaches. Analysis and numerical experiments reveal that the first strategy is more accurate and efficient than the latter. The block structure in the third type of algebraic systems is due to a fine-coarse splitting of the unknowns. The inverse of the pivot block is approximated by a sparse matrix which is assembled from local, exactly inverted matrices. Numerical experiments and analysis of the approximation show that it is robust with respect to problem size and coefficient jumps

Analytic prediction of electromagnetic behaviour

The amount of electrical loads and the complexity of the electric system in a vehicle is increasing at the same time as the allowed development time is getting shorter. Possibilities to predict the electromagnetic behaviour is therefore of great importance. In this paper, a method for determining the parasitic components affecting crosstalk in a cable harness is proposed. The method suggests that a more complex ground structure should for calculation purposes be replaced by equivalent ground planes. Calculated parameter values are compared to values gained from simulation in a circuit model for investigation of crosstalk. It is shown that also an approximation of the parasitic components will give a good comprehension of the crosstalk effects in the cable harness

How to control SiC BJT with high efficiency?

SiC Bipolar Junction Transistor has many benefits such as low on-state voltage drop, high switching speed and high maximum operating temperature. However it has one major disadvantage that it needs current to be turned on. This causes an increased power requirement of the driver circuit compared to voltage controlled devices like MOSFETs and IGBTs. The proposed driving concept is based on a verified Darlington typology together with a voltage compensation component which gives a solution to this problem. The proposed driving concept is evaluated by both simulation and experimental results. The investigation of parallel connection of SiC BJT transistors that use the proposed drive concept is also included in this paper