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Survey of period infinite element developments The first infinite elements for periodic wave problems, as stated in Part 1, were developed by Bettess and Zienkiewicz, the earliest publication being in 1975. These applications were of ‘decay function’ type elements and were used in surface waves on water problems. This was soon followed by an application by Saini et al., to dam‐reservoir interaction, where the waves are pressure waves in the water in the reservoir. In this case both the solid displacements and the fluid pressures are complex valued. In 1980 to 1983 Medina and co‐workers and Chow and Smith successfully used quite different methods to develop infinite elements for elastic waves. Zienkiewicz et al. published the details of the first mapped wave infinite element formulation, which they went on to program, and to use to generate results for surface wave problems. In 1982 Aggarwal et al. used infinite elements in fluid‐structure interaction problems, in this case plates vibrating in an unbounded fluid. In 1983 Corzani used infinite elements for electric wave problems. This period also saw the first infinite element applications in acoustics, by Astley and Eversman, and their development of the ‘wave envelope’ concept. Kagawa applied periodic infinite wave elements to Helmholtz equation in electromagnetic applications. Pos used infinite elements to model wave diffraction by breakwaters and gave comparisons with laboratory photogrammetric measurements of waves. Good agreement was obtained. Huang also used infinite elements for surface wave diffraction problems. Davies and Rahman used infinite elements to model wave guide behaviour. Moriya developed a new type of infinite element for Helmholtz problem. In 1986 Yamabuchi et al. developed another infinite element for unbounded Helmholtz problems. Rajapalakse et al. produced an infinite element for elastodynamics, in which some of the integrations are carried out analytically, and which is said to model correctly both body and Rayleigh waves. Imai et al. gave further applications of infinite elements to wave diffraction, fluid‐structure interaction and wave force calculations for breakwaters, offshore platforms and a floating rectangular caisson. Pantic et al. used infinite elements in wave guide computations. In 1986 Cao et al. applied infinite elements to dynamic interaction of soil and pile. The infinite element is said to be ‘semi‐analytical’. Goransson and Davidsson used a mapped wave infinite element in some three dimensional acoustic problems, in 1987. They incorporated the infinite elements into the ASKA code. A novel application of wave infinite elements to photolithography simulation for semiconductor device fabrication was given by Matsuzawa et al. They obtained ‘reasonably good’ agreement with observed photoresist profiles. Häggblad and Nordgren used infinite elements in a dynamic analysis of non‐linear soil‐structure interaction, with plastic soil elements. In 1989 Lau and Ji published a new type of 3‐D infinite element for wave diffraction problems. They gave good results for problems of waves diffracted by a cylinder and various three dimensional structures.

This paper is concerned with static problems, i.e. those which do not change with time. Dynamic problems will be considered in a sequel. The historical development of infinite elements is described. The two main developments, decay function infinite elements and mapped infinite elements, are described in detail. Results obtained using various infinite elements are given, followed by a discussion of possibilities and likely developments.

This paper is concerned with infinite elements for dynamic problems, that is, those which change in time. It is a sequel to our earlier paper on static problems. The paper is in a number of sections. The first is an introduction. In the second the state‐of‐the‐art review of infinite elements is updated. In the third, ‘added mass’ type effects are considered. In the fourth, time dependent problems of the diffusion type, which only involve the first time derivative are considered. Wave problems are considered in the fifth and the necessary radiation conditions for such problems are summarized. Section six deals with dynamic problems of a repetitive nature, that is periodic or harmonic problems. In section seven completely transient problems are dealt with and some fundamental difficulties are noted. Conclusions are drawn in section eight.

A profile solver which factorizes the profile matrix K into the form LDLT, is described. D is a diagonal matrix and L is a lower triangular matrix. LT is stored by columns, using a steering vector, to locate the elements. In addition a fixity vector is used. This indicates which degrees of freedom are free and which are fixed. A main program uses a random number generator to set up test data. Full listings are given, together with information on how to get a copy of the program.

A simple discrete vortex program written in the Occam language for implementation on transputers is presented. The programming methodology and logic are described, with an emphasis on the use of parallel features. Listings of procedures discussed in the text are given.

The use of algebraic languages such as REDUCE makes possible the automatic generation, from fairly concise data, of the main families of two and three dimensional C0 continuous finite element shape functions, with a high confidence in their correctness. This paper gives a tutorial introduction to the REDUCE language and describes how it was used to generate shape function routines.

In recent years attention has turned from conventional ‘von Neumann’ computers to totally new computer architectures. Many surveys of these developments are available and a number of conferences have been held on the topic. One extremely interesting development is the transputer, or so‐called computer on a chip, designed and developed by the British company, Inmos. This exciting innovation has been backed by the SERC, who have launched an initiative entitled ‘Engineering Applications of Transputers’. Under the terms of this initiative, it is possible for British academics to obtain short term loans of transputer equipment, in order to evaluate it and to prepare more extensive research proposals, which would exploit the transputer. The authors obtained a loan of a single transputer board, for 8 months and were able to develop some programs for finite element analysis and for discrete vortex modelling of fluid flows. This paper describes the work carried out on finite elements. The purpose of the paper is to list and describe some simple working finite element programs written in Occam and to draw attention to their novel features.

The formation of the well known element mass, geometric stiffness and stiffness matrices based on Hermite polynomials can be very easily automated using Computer Algebra systems. The algebraic language REDUCE has been used to obtain the algebraic expressions for such matrices in one and two dimensions and to automatically produce FORTRAN code. The program developed can derive the matrices for any number of nodes in the element. The aim is to demonstrate how the Computer Algebra system can greatly reduce the effort in forming these classical matrices. It can thus be used as a teaching aid.

The purpose of this paper is to propose a stable high-order absorbing boundary condition (ABC) based on new continued fraction for scalar wave propagation in 2D and 3D unbounded layers.

The ABC is obtained based on continued fraction (CF) expansion of the frequency-domain dynamic stiffness coefficient (DtN kernel) on the artificial boundary of a truncated infinite domain. The CF which has been used to the thin layer method in [69] will be applied to the DtN method to develop a time-domain high-order ABC for the transient scalar wave propagation in 2D. Furthermore, a new stable composite-CF is proposed in this study for 3D unbounded layers by nesting the above CF for 2D layer and another CF.

The ABS has been transformed from frequency to time domain by using the auxiliary variable technique. The high-order time-domain ABC can couple seamlessly with the finite element method. The instability of the ABC-FEM coupled system is discussed and cured.

This manuscript establishes a stable high-order time-domain ABC for the scalar wave equation in 2D and 3D unbounded layers, which is based on the new continued fraction. The high-order time-domain ABC can couple seamlessly with the finite element method. The instability of the coupled system is discussed and cured.

A boundary element method has been developed to calculate the added mass matrix of fluid coupled structures in the case when the fluid is assumed to be compressible and inviscid. The potential flow is represented by a double layer density with linear interpolation functions. A linear set of equations for the fluid motion is obtained by Galerkin's procedure. The added mass matrix is not symmetric but a symmetrization procedure is established. The method has been implemented into a computer code for two‐dimensional geometries, whose results are presented here. A comparison with the analytical results already shows excellent agreement for coarse discretizations.