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Showing 1 to 14 of 14 for “"Differential Algebraic Equations (DAEs)"”.
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Approximation Methods for the Consistent Initialization of Differential-Algebraic Equations
The algebraic constraints in a system of differential-algebraic equations (DAEs) impose a consistency requirement on the initial values that can be difficult to satisfy. In this thesis the consistency requirement is characterized by a system of equations. An approximation method is introduced for …
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Applications and numerical investigation of differential-algebraic equations
Differential-algebraic equations (DAEs) result in many areas of science and engineer- ing. In this thesis, numerical methods for solving DAEs are compared for two prob- lems, energy-economic models and traffic flow models. An energy-economic model is presented based on the Hubbert model of oil …
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Waveform relaxation methods for the simulation of systems of differential algebraic equations with applications to electric power systems
… terminals are kept intact, yielding a set of differential/algebraic equations (DAEs). In addition to power systems, systems of differential/algebraic equations arise in connection with singular perturbation, control theory, robot systems, and many other applications in the fields of mechanical …
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Theory and Application of a Class of Abstract Differential-Algebraic Equations
… and existence of solutions for ordinary differential-algebraic equations (DAEs). Because of the geometric and operator-theoretic aspects of this particular method, it can be extended to the case of infinite-dimensional abstract DAEs. For example, partial differential equations (PDEs) are …
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Qualitative and Quantitative Investigation of Planar Multibody Dynamics Encompassing GSSSS Family of Algorithms - A Novel In-depth Look
… wide variety of time integration methods for the differential-algebraic equations (DAEs) inherent to these systems. The vast majority of these methods require refor- mulation of the natural index 3 equations of motion leading to additional computational cost and the need to control drift …
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Simulating, Controlling, and Understanding Lithium-ion Battery Models
… PET typically contains several hundred nonlinear differential-algebraic equations (DAEs) after discretization. This package is designed from a systems engineering perspective to be robust and highly efficient, about 100–1000x faster than other available implementations of PET while maintaining the …
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Direct Sensitivity Analysis of Spatial Multibody Systems with Joint Friction
… systems have to be modeled by highly non-linear differential algebraic equations (DAEs) that are difficult to solve using numerical methods. The sensitivity analysis of such systems and the subsequent design optimization is a novel area of research that has been explored in this work. The …
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Exponential Integrators for the Incompressible Navier-Stokes Equations
… integration of the incompressible Navier-Stokes equations (NSE). The method is based on a projection onto the subspace of divergence-free (incompressible) functions interleaved with a Krylov-based exponential time integration (KBEI). These time integration methods provide a high order accurate, …
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Reachability analysis and deterministic global optimization of differential-algebraic systems
Systems of differential-algebraic equations (DAEs) are used to model an incredible variety of dynamic phenomena. In the chemical process industry in particular, the numerical simulation of detailed DAE models has become a cornerstone of many core activities including, process development, economic …
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Numerical Methods for Simulation and Optimization of Chemically Reacting Flows in Catalytic Monoliths
… dynamics are modelled by the boundary layer equations (BLEs), which are a large system of parabolic partial differential equations (PDEs) with highly nonlinear boundary conditions arising from the coupling of surface processes with the flow field inside the channel. The BLEs are obtained by …
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Multiscale Modeling, Reformulation, and Efficient Simulation of Lithium-Ion Batteries
… are described using several nonlinear partial differential equations, simulating battery models can quickly become computationally expensive. Thus, much of this work focuses on reformulating the battery model to improve simulation efficiency, allowing for use to solve problems which require …
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Tools for dynamic model development
… in chemical kinetic systems. Ordinary differential equations (ODEs) are sufficient to model many dynamic systems, such as those listed above. Differential-algebraic equations (DAEs) can be used to model any ODE system and can also contain algebraic equations, such as those for chemical …
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Index analysis of semistate systems without passivity restrictions
… increasing interest on semistate models based on differential-algebraic equations (DAEs) for the analysis and simulation of non-linear electrical circuits. Modelling techniques such as Node Tableau Analysis (NTA), Augmented Nodal Analysis (ANA), or Modified Nodal Analysis (MNA), the latter used …
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Parametric Optimal Design Of Uncertain Dynamical Systems
… is used to solve the corresponding uncertain differential equations. This technique is significantly faster computationally than traditional sampling methods and makes the construction of a parametric optimal design framework for uncertain systems feasible. The novel framework allows to …