A multigrid solver for the semiconductor equations

We present a multigrid solver for the exponential fitting method. The solver is applied to the current continuity equations of semiconductor device simulation in two dimensions. The exponential fitting method is based on a mixed finite element discretization using the lowest-order Raviart-Thomas triangular element. This discretization method yields a good approximation of front layers and guarantees current conservation. The corresponding stiffness matrix is an M-matrix. 'Standard' multigrid solvers, however, cannot be applied to the resulting system, as this is dominated by an unsymmetric part, which is due to the presence of strong convection in part of the domain. To overcome this difficulty, we explore the connection between Raviart-Thomas mixed methods and the nonconforming Crouzeix-Raviart finite element discretization. In this way we can construct nonstandard prolongation and restriction operators using easily computable weighted L(exp 2)-projections based on suitable quadrature rules and the upwind effects of the discretization. The resulting multigrid algorithm shows very good results, even for real-world problems and for locally refined grids

On the choice of initial guesses for the Newton-Raphson algorithm

The initialization of equation-based differential-algebraic system models, and more in general the solution of many engineering and scientific problems, require the solution of systems of nonlinear equations. Newton-Raphson's method is widely used for this purpose; it is very efficient in the computation of the solution if the initial guess is close enough to it, but it can fail otherwise. In this paper, several criteria are introduced to analyze the influence of the initial guess on the evolution of Newton-Raphson's algorithm and to identify which initial guesses need to be improved in case of convergence failure. In particular, indicators based on first and second derivatives of the residual function are introduced, whose values allow to assess how much the initial guess of each variable can be responsible for the convergence failure. The use of such criteria, which are based on rigorously proven results, is successfully demonstrated in three exemplary test cases.Comment: Version accepted for publication on Applied Mathematics and Computatio

Concepts of Ethical Leadership and their Potential Implementation in Organisations: An Operational Perspective

This study links ethical leadership theory to the implementation of improved leadership practices and examines whether ethical leadership characteristics actually exist, particularly in highly operational environments.The study analyses how ethical leadership can be embedded by process, by applied leadership (role modelling), and by changing culture and climate. The conclusion reveals that all three approaches are needed for an implementation and depend on middle managers, otherwise no organisational transformation is possible.The research design of this qualitative study analyses data from 100 in-depth interviews using inductive categorisation, aiming to retrieve deep, rich and unprompted data from a highly developed and advanced production facility. The ethical leadership characteristics, and evidence specific influences on leadership behaviour, revealing 14 perceived leadership issues resulting in a leadership climate which negatively influences motivation, performance, and corporate culture.These issues were found to be responsible for deteriorating work climate, motivation, morale, and team spirit. Particularly favouritism, inequalities, shouting, blaming, internal competition and unclear strategies ruin motivation, employee health, and co-operation.Concerning the implementation of a better suited leadership culture, a research framework model is developed, integrating transformational change and leadership.Findings document that the influence of middle managers acting as role models seems to be greater than research suggests. Key findings also show that individual leadership development without changing the corporate realities is not sufficient to implement ethical strategies. Neglecting to actively control the leadership climate can have devastating effects even for very successful operations.Considering the pressure of goal attainment in highly operational areas, an absence of unethical behaviour can already be seen as a success for leaders.Finally, a change process sequence for shaping leadership climate was identified.These research results are highly relevant for organisations and leaders wishing to be engaged in improving their leadership quality

Concepts of Ethical Leadership and their Potential Implementation in Organisations: An Operational Perspective

This study links ethical leadership theory to the implementation of improved leadership practices and examines whether ethical leadership characteristics actually exist, particularly in highly operational environments.The study analyses how ethical leadership can be embedded by process, by applied leadership (role modelling), and by changing culture and climate. The conclusion reveals that all three approaches are needed for an implementation and depend on middle managers, otherwise no organisational transformation is possible.The research design of this qualitative study analyses data from 100 in-depth interviews using inductive categorisation, aiming to retrieve deep, rich and unprompted data from a highly developed and advanced production facility. The ethical leadership characteristics, and evidence specific influences on leadership behaviour, revealing 14 perceived leadership issues resulting in a leadership climate which negatively influences motivation, performance, and corporate culture.These issues were found to be responsible for deteriorating work climate, motivation, morale, and team spirit. Particularly favouritism, inequalities, shouting, blaming, internal competition and unclear strategies ruin motivation, employee health, and co-operation.Concerning the implementation of a better suited leadership culture, a research framework model is developed, integrating transformational change and leadership.Findings document that the influence of middle managers acting as role models seems to be greater than research suggests. Key findings also show that individual leadership development without changing the corporate realities is not sufficient to implement ethical strategies. Neglecting to actively control the leadership climate can have devastating effects even for very successful operations.Considering the pressure of goal attainment in highly operational areas, an absence of unethical behaviour can already be seen as a success for leaders.Finally, a change process sequence for shaping leadership climate was identified.These research results are highly relevant for organisations and leaders wishing to be engaged in improving their leadership quality

Generation of Sparse Jacobians for the Function Mock-Up Interface 2.0

Derivatives, or Jacobians, are commonly required by numerical algorithms. Access to accurate Jacobians often improves the performance and robustness of algorithms, and in addition, efficient implementation of Jacobian computations can reduce the over-all execution time. In this paper, we present methods for computing Jacobians in the context of the Functional Mock-up Interface (FMI), and Modelica. Two prototype implementations, in JModelica.org and OpenModelica are presented and compared in industrial benchmarks

Design And Realization Of An Automated Test-Stand For Variable Capacity Household Compressors

In Switzerland the efficiency of household refrigerators has to be proved by the manufacturer to get the energy label for the devices. The efficiency is tested in the beginning of the lifetime of the fridge and each component, respectively. Especially the compressor might assumedly reach its best performance not before some hours of operation. The exact knowledge about this characteristic is quite important for the manufacturer to optimize the products. Therefore, an automated compressor test stand was designed and built to test variable speed compressors on their evolution of isentropic and volumetric efficiencies. The test stand features three electronic expansion valves to control high and low pressure, and the suction gas temperature of the compressor, automatically. If necessary, an additional heater compensates for the non-isenthalpic pressure drop through the mass flow meter at the discharge of the compressor to enable high suction gas temperatures. Also, the ambient temperature of the device under test is controlled in its separate compartment. The power consumption of the compressor is detected with and without the controller to get additional information. The testing range is 20…200 W cooling capacity with pressures of the refrigerant R600a down to the corresponding evaporation temperature of -35°C and condensing temperatures up to 55°C. The test-stand is equipped with high precision sensors to ensure measurement uncertainties of volumetric and isentropic efficiencies smaller than 5% over the whole range. This paper reports the design of the test stand as well as the control of the system

Symbolic Initialization of Over-determined Higher-index Models

Abstract The quantity of initial equations required in an objectoriented model can only be determined at system level. Since Modelica models are generally designed by components, it is difficult to calculate the amount of initial equations needed at system level, especially when changes are applied to the model, e.g. by adding or removing components. Therefore, it is more convenient to define initial equations at component level. Due to component connections, algebraic dependencies between states may be introduced, which eventually lead to the removal of states when symbolic index reduction algorithms are applied. In this process, the corresponding initial equations are not automatically removed, which results in an over-determined initial system. This paper describes an algorithm that detects such redundant equations and determines if they are consistent or not. Consistent redundant initial equations can thus be removed automatically, and inconsistent ones can be reported to the modeler. A prototype of the algorithm is implemented in OpenModelica, tested on several representative cases, and compared to previously presented concepts