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The purpose of this paper is to present the method of lines (MOL) solution of the stimulated Brillouin scattering (SBS) equations (a system of three first-order hyperbolic partial differential equations (PDEs)), describing the three-wave interaction resulting from a coupling between light and acoustic waves. The system has complex numbers and boundary values.

System of three first-order hyperbolic PDEs are first transformed and then spatially discretized. Superbee flux limiter is proposed to offset numerical damping and dispersion, brought on by the low order approximation of spatial derivatives in the PDEs. In order to increase computational efficiency, the structured structure of the PDE Jacobian matrix is identified and a sparse integration algorithm option of the ordinary differential equation (ODE) solvers is used. The flux limiter based on higher order approximations eliminates numerical oscillation. Examples are presented, and the performance of the Matlab ODE solvers is evaluated by comparison.

This type of solution provides a rapid means of investigating SBS as a tool in fiber optic sensing.

To the best of the authors' knowledge, MOL solution is proposed for the first time for the modeling of three-wave interaction in a SBS-based fiber optic sensor.

This paper aims to develop a meshfree algorithm based on local radial basis functions (RBFs) combined with the differential quadrature (DQ) method to provide numerical approximations of the solutions of time-dependent, nonlinear and spatially one-dimensional reaction-diffusion systems and to capture their evolving patterns. The combination of local RBFs and the DQ method is applied to discretize the system in space; implicit multistep methods are subsequently used to discretize in time.

In a method of lines setting, a meshless method for their discretization in space is proposed. This discretization is based on a DQ approach, and RBFs are used as test functions. A local approach is followed where only selected RBFs feature in the computation of a particular DQ weight.

The proposed method is applied on four reaction-diffusion models: Huxley’s equation, a linear reaction-diffusion system, the Gray–Scott model and the two-dimensional Brusselator model. The method captured the various patterns of the models similar to available in literature. The method shows second order of convergence in space variables and works reliably and efficiently for the problems.

The originality lies in the following facts: A meshless method is proposed for reaction-diffusion models based on local RBFs; the proposed scheme is able to capture patterns of the models for big time T; the scheme has second order of convergence in both time and space variables and Nuemann boundary conditions are easy to implement in this scheme.

This paper discusses algorithms for large displacement analysis of interconnected flexible and rigid multibody systems. Hydrostatic and hydrodynamic loads for systems being submerged in water are also considered. The systems may consist of cables and beams and may combine very flexible parts with rigid parts. Various ways of introducing structural joints are discussed. A special implementation of the Hilber‐Hughes‐Taylor time integration scheme for constrained non‐linear systems is outlined. The formulation is general and allows for displacements and rotational motion of unlimited size. Aspects concerning efficient solution of constrained dynamic problems are discussed. These capabilities have been implemented in a general purpose non‐linear finite element program. Applications involving static and dynamic analysis of a bi‐articulated tower and a floating tripod platform kept in place by three anchor lines are discussed.

Transient eddy current formulations based on the Finite Integration Technique (FIT) for the magneto‐quasistatic regime are extended to include motional induction effects of moving conductors with simple geometries by different approaches. A new regularization of the formulation using discrete grad‐div augmentation of the curlcurl formulation is presented and tested. To improve the implicit time integration process, several schemes for an error controlled variable time step selection are presented and for the repetitive solution of the arising large sparse systems of equations a sparse direct solver is compared to iterative methods such as a preconditioned conjugate gradient method and a new algebraic multigrid solver, which is aware of the curlcurl nullspace.

Partitioned analysis is a method by which sets of time‐dependent ordinary differential equations for coupled systems may be numerically integrated in tandem, thereby avoiding brute‐force simultaneous solution. The coupled systems addressed pertain to fluid—structure, fluid—soil, soil—structure, or even structure—structure interaction. The paper describes the partitioning process for certain discrete‐element equations of motion, as well as the associated computer implementation. It then delineates the procedure for designing a partitioned analysis method in a given application. Finally, examples are presented to illustrate the concepts. It is seen that a key element in the implementation of partitioned analysis is the use of integrated, as opposed to monolithic software.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

Model order reduction (MOR) has been widely used in the electric networks but little has been done to reduce higher index differential algebraic equations (DAEs). The paper aims to discuss these issues.

Most methods first do an index reduction before reducing a higher DAE but this can lead to a loss of physical properties of the system.

The paper presents a MOR method for DAEs called the index-aware MOR (IMOR) which can reduce a DAE while preserving its physical properties such as the index. The feasibility of this method is tested on real-life electric networks.

MOR has been widely used to reduce large systems from electric networks but little has been done to reduce higher index DAEs. Most methods first do an index reduction before reducing a large system of DAEs but this can lead to a loss of physical properties of the system. The paper presents a MOR method for DAEs called the IMOR which can reduce a DAE while preserving its physical properties such as the index. The feasibility of this method is tested on real-life electric networks.

The purpose of this paper is to review the mutual coupling of electromagnetic fields in the magnetic vector potential formulation with electric circuits in terms of (modified) nodal and loop analyses. It aims for an unified and generic notation.

The coupled formulation is derived rigorously using the concept of winding functions. Strong and weak coupling approaches are proposed and examples are given. Discretization methods of the partial differential equations and in particular the winding functions are discussed. Reasons for instabilities in the numerical time domain simulation of the coupled formulation are presented using results from differential-algebraic-index analysis.

This paper establishes a unified notation for different conductor models, e.g. solid, stranded and foil conductors and shows their structural equivalence. The structural information explains numerical instabilities in the case of current excitation.

The presentation of winding functions allows to generically describe the coupling, embed the circuit equations into the de Rham complex and visualize them by Tonti diagrams. This is of value for scientists interested in differential geometry and engineers that work in the field of numerical simulation of field-circuit coupled problems.

Discusses the 27 papers in ISEF 1999 Proceedings on the subject of electromagnetisms. States the groups of papers cover such subjects within the discipline as: induction machines; reluctance motors; PM motors; transformers and reactors; and special problems and applications. Debates all of these in great detail and itemizes each with greater in‐depth discussion of the various technical applications and areas. Concludes that the recommendations made should be adhered to.

This paper aims to propose an adaptive method for the numerical solution of the shallow water equations (SWEs). The authors provide an arbitrary high-order method using high-order spline wavelets. Furthermore, they use a non-linear shock capturing (SC) diffusion which removes the necessity of post-processing.

The authors use a space-time weak formulation of SWEs which exploits continuous Galerkin (cG) in space and discontinuous Galerkin (dG) in time allowing time stepping, also known as cGdG. Such formulations along with SC term have recently been proved to ensure the stability of fully discrete schemes without scarifying the accuracy. However, the resulting scheme is expensive in terms of number of degrees of freedom (DoFs). By using natural adaptivity of wavelet expansions, the authors devise an adaptive algorithm to reduce the number of DoFs.

The proposed algorithm uses DoFs in a dynamic way to capture the shocks in all time steps while keeping the representation of approximate solution sparse. The performance of the proposed scheme is shown through some numerical examples.

An incorporation of wavelets for adaptivity in space-time weak formulations applied for SWEs is proposed.