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Stateflow (developed by MathWorks) is a control logic tool used to model reactive systems via state machines and flow charts within a Simulink model. Stateflow uses a variant of the finite-state machine notation established by David Harel, enabling the representation of hierarchy, parallelism and history within a state chart.
Simulink is a MATLAB-based graphical programming environment for modeling, simulating and analyzing multidomain dynamical systems. Its primary interface is a graphical block diagramming tool and a customizable set of block libraries .
The transmission-line matrix (TLM) method is a space and time discretising method for computation of electromagnetic fields. It is based on the analogy between the electromagnetic field and a mesh of transmission lines .
Matrix-free conjugate gradient method has been applied in the non-linear elasto-plastic finite element solver. [7] Solving these equations requires the calculation of the Jacobian which is costly in terms of CPU time and storage. To avoid this expense, matrix-free methods are employed.
This may be written more succinctly in matrix operator notation as, = where Y is a column vector of the outputs, G is a matrix of the transfer functions, and U is a column vector of the inputs. In many cases, the system under consideration is a linear time-invariant (LTI) system.
Consequently, () is a matrix with the dimension which contains transfer functions for each input output combination. Due to the simplicity of this matrix notation, the state-space representation is commonly used for multiple-input, multiple-output systems.
It is similar to a block diagram or signal-flow graph, with the major difference that the arcs in bond graphs represent bi-directional exchange of physical energy, while those in block diagrams and signal-flow graphs represent uni-directional flow of information. Bond graphs are multi-energy domain (e.g. mechanical, electrical, hydraulic, etc ...
The admissible limiter region for second-order TVD schemes is shown in the Sweby Diagram opposite, [9] and plots showing limiter functions overlaid onto the TVD region are shown below. In this image, plots for the Osher and Sweby limiters have been generated using β = 1.5 {\displaystyle \beta =1.5} .