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To provide an analysis of transient heat conduction, which is solved using different iterative solvers for graduate and postgraduate students (researchers) which can help them develop their own research.

Three‐dimensional transient heat conduction in homogeneous materials using different time‐stepping methods such as finite difference (Θ explicit, implicit and Crank‐Nicolson) and finite element (weighted residual and least squared) methods. Iterative solvers used in the paper are conjugate gradient (CG), preconditioned gradient, least square CG, conjugate gradient squared (CGS), preconditioned CGS, bi‐conjugate gradient (BCG), preconditioned BCG, bi‐conjugate gradient stabilized (BCGSTAB), reconditioned BCGSTAB and Gaussian elimination with incomplete Cholesky factorization.

Provides information on which time‐stepping method is the most accurate, which solver is the fastest to solve a symmetric and positive system of linear matrix equations of all those considered.

Fortran 90 code given as an abstract can be very useful for graduate and postgraduate students to develop their own code.

This paper offers practical help to an individual starting his/her research in the finite element technique and numerical methods.

The purpose of this paper is to find the best solver for parallelizing particle methods based on solving Pressure Poisson Equation (PPE) by taking Moving Particle Semi-Implicit (MPS) method as an example because the solution for PPE is usually the most time-consuming part difficult to parallelize.

To find the best solver, the authors compare six Krylov solvers, namely, Conjugate Gradient method (CG), Scaled Conjugate Gradient method (SCG), Bi-Conjugate Gradient Stabilized (BiCGStab) method, Conjugate Gradient Squared (CGS) method with Symmetric Lanczos Algorithm (SLA) method and Incomplete Cholesky Conjugate Gradient method (ICCG) in terms of convergence, time consumption, parallel efficiency and memory consumption for the semi-implicit particle method. The MPS method is parallelized by the hybrid Open Multi-Processing (OpenMP)/Message Passing Interface (MPI) model. The dam-break flow and channel flow simulations are used to evaluate the performance of different solvers.

It is found that CG converges stably, runs fastest in the serial way, uses the least memory and has highest OpenMP parallel efficiency, but its MPI parallel efficiency is lower than SLA because SLA requires less synchronization than CG.

With all these criteria considered and weighed, the recommended parallel solver for the MPS method is CG.

In this paper we investigate the performance of CGS, BCGSTAB and GMRES with ILU preconditioner for solving convection‐diffusion problems. Numerical experiments indicate that BCGSTAB appears to be an efficient and stable method. CGS sometimes suffers from severe numerical instability. GMRES shows a higher suitability and stability but the overall convergence rate may be lower.

The purpose of this paper is to present the efficient iterative methods for solving linear complementarity problems (LCP), using a class of pre-conditioners.

By using the concept of solving the fixed-point system of equations associated to the LCP, pre-conditioning techniques and Krylov subspace methods the authors design some projected methods to solve LCP. Furthermore, within the computational framework, some models of pre-conditioners candidates are investigated and evaluated.

The proposed algorithms have a simple and graceful structure and can be applied to other complementarity problems. Asymptotic convergence of the sequence generated by the method to the unique solution of LCP is proved, along with a result regarding the convergence rate of the pre-conditioned methods. Finally, a computational comparison of the standard methods against pre-conditioned methods based on Example 1 is presented which illustrate the merits of simplicity, power and effectiveness of the proposed algorithms.

Comparison between the authors' methods and other similar methods for the studied problem shows a remarkable agreement and reveals that their models are superior in point of view rate of convergence and computing efficiency.

For solving LCP more attention has recently been paid on a class of iterative methods called the matrix-splitting such as AOR, MAOR, GAOR, SSOR, etc. But up to now, no paper has discussed the effect of pre-conditioning technique for matrix-splitting methods in LCP. So, this paper is planning to fill in this gap and the authors use a class of pre-conditioners with iterative methods and analyze the convergence of these methods for LCP.

The purpose of this paper is to examine the modeling of simultaneous heat and mass transfer under dehumidifying conditions. Moist air cooling in tube‐fin exchangers is investigated using a finite element technique.

The model requires the solution of a conjugate problem, since interface temperatures must be calculated at the same time as temperature distributions in adjacent fluid and solid regions. The energy equation is solved in the whole domain, including the solid region, and the latent heat flux on the surfaces where condensation takes place is taken into account by means of an additional internal boundary condition.

Thermal performances for different Reynolds numbers of a typical two‐row tube‐fin exchanger are numerically analysed, for both in‐line and staggered arrangements of tubes. The results justify the great importance that the ratio between latent and overall rates of heat transfer has in the design of compact heat exchangers.

In this work, the capabilities of the proposed methodology to deal with industrial applications in the field of compact exchangers are outlined.

The paper presents an effective approach to the solution of conjugate conduction and convection problems with simultaneous heat and mass transfer. The formulation is completely general, even if the finite element method is used in the calculations.

The purpose of this paper is to propose novel factored approximate sparse inverse schemes and multi-level methods for the solution of large sparse linear systems.

The main motive for the derivation of the various generic preconditioning schemes lies to the efficiency and effectiveness of factored preconditioning schemes in conjunction with Krylov subspace iterative methods as well as multi-level techniques for solving various model problems. Factored approximate inverses, namely, Generic Factored Approximate Sparse Inverse, require less fill-in and are computed faster due to the reduced number of nonzero elements. A modified column wise approach, namely, Modified Generic Factored Approximate Sparse Inverse, is also proposed to further enhance performance. The multi-level approximate inverse scheme, namely, Multi-level Algebraic Recursive Generic Approximate Inverse Solver, utilizes a multi-level hierarchy formed using Block Independent Set reordering scheme and an approximation of the Schur complement that results in the solution of reduced order linear systems thus enhancing performance and convergence behavior. Moreover, a theoretical estimate for the quality of the multi-level approximate inverse is also provided.

Application of the proposed schemes to various model problems is discussed and numerical results are given concerning the convergence behavior and the convergence factors. The results are comparatively better than results by other researchers for some of the model problems.

Further enhancements are investigated for the proposed factored approximate inverse schemes as well as the multi-level techniques to improve quality of the schemes. Furthermore, the proposed schemes rely on the definition of multiple parameters that for some problems require thorough testing, thus adaptive techniques to define the values of the various parameters are currently under research. Moreover, parallel schemes will be investigated.

The proposed approximate inverse preconditioning schemes as well as multi-level schemes are efficient computational methods that are valuable for computer scientists and for scientists and engineers in engineering computations.

This study proposes to develop and investigate different iterative solvers for non‐Newtonian flow equations.

Existing approaches for the time discretization of the flow equation and for an iterative solution of the discrete systems are discussed. Ideas for further development of existing preconditioners are proposed, implemented and investigated numerically.

A two‐level preconditioning, consisting of a transformation of the original system in the first step and subsequent preconditioning of the transformed system is suggested. The GMRES iterative method, which usually performs well when applied to academic problems, showed dissatisfactory performance for the type of industrial flow simulations investigated in this work. It was found that the BiCGStab method performed best in the tests presented here.

The iterative solvers considered here were investigated only for a certain class of polymer flows. More detailed studies for other non‐Newtonian flows should be carried out.

The work presented in this paper fills a gap related to the usage of efficient iterative methods for non‐Newtonian flow simulations.

Selective laser melting (SLM) is a major additive manufacturing (AM) process in which laser beams are used as the heat source to melt and deposit metals in a layerwise fashion to enable the construction of components of arbitrary complexity. The purpose of this paper is to develop a framework for accurate and fast prediction of the temperature distribution during the SLM process.

A fast computation tool is proposed for thermal analysis of the SLM process. It is based on the finite volume method (FVM) and the quiet element method to allow the development of customized functionalities at the source level. The results obtained from the proposed FVM approach are compared against those obtained from the finite element method (FEM) using a well-established commercial software, in terms of accuracy and efficiency.

The results show that for simulating the SLM deposition of a cubic block with 81,000, 189,000 and 297,000 cells, the computation takes about 767, 3,041 and 7,054 min, respectively, with the FEM approach; while 174, 679 and 1,630 min with the FVM code. This represents a speedup of around 4.4x. Meanwhile, the average temperature difference between the two is below 6%, indicating good agreement between them.

The thermal field for the multi-track and multi-layer SLM process is for the first time computed by the FVM approach. This pioneering work on comparing FVM and FEM for SLM applications implies that a fast and simple computing tool for thermal analysis of the SLM process is within the reach, and it delivers comparable accuracy with significantly higher computational efficiency. The research results lay the foundation for a potentially cost-effective tool for investigating the fundamental microstructure evolution, and also optimizing the process parameters in the SLM process.

The development of electrical machines is nowadays closely related to the knowledge of the electromagnetic fields throughout the different parts of a machine. Although a machine is often of complicated geometrical structure and of different, mostly nonlinear materials, modern numerical methods and the related software allow calculation of the fields in 2D models and several 3D cases precisely enough in order to derivate from them quantities like energy density distribution, the torque behaviour and characteristics like load and no load. The paper will at first compare numerical methods suited for electromagnetic field calculation in electrical machines. The following topic deals with adaptive mesh generation playing an important role to save computer memory and cpu time. Then examples like a Switched Reluctance Machine, an Asynchronous Machine and a Stepping Motor are shown concerning the results of field calculation. It is shown that anisotropy may have to be taken into account, and finally it is shown that field calculation enables the shape optimization of a machine.

The insulated gate bipolar transistor (IGBT) is an increasingly used power transistor which has the advantage over the more conventional DMOS structure of achieving a lower on‐resistance through the high‐injection of electrons and holes into the drift region thereby causing conductivity modulation and a lowering of the electrical resistance.