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Designing of induction heating, or, generally electro technological installations, requires mathematical modeling for solving problems related to various physical phenomena, including electromagnetic (EM), thermal, mechanical, fluidic, and metallurgical fields. This article focuses on the solution of Maxwell's equations (MEs) and provides some basic information regarding the heat transfer and fluid equations, because these physical phenomena usually are strongly coupled to magnetic and electric fields. The solutions are usually obtained by using specific numerical methods such as finite-element method, finite difference method, boundary-element method or volume-integral method, and direct-solution method. The article also discusses the typical structure of commercial codes (preprocessor, solver, and postprocessor) to solve field problems mainly in finite-element method.

Analytical transmission electron microscopy (ATEM) is unique among materials characterization techniques as it enables essentially the simultaneous examination of microstructural features through high-resolution imaging and the acquisition of chemical and crystallographic information from small regions of the specimen. This article illustrates the effectiveness of the technique in solving materials problems. The first section of the article provides information on analytical electron microscope (AEM) and its basic operational characteristics as well as on electron optics, electron beam/specimen interactions and the generation of a signal, signal detectors, electron diffraction, imaging, x-ray microanalysis, electron energy loss spectroscopy, and sample preparation. The second section consists of 12 examples, each illustrating a specific type of materials problem that can be solved, at least in part, with AEM.

The process of optimization involves choosing the best solution from a pool of potential candidate solutions. This article provides a description of some classes of problems and the optimization methods that solve them. These problems include the deterministic single-objective problem, the deterministic multiobjective problem, and the nondeterministic, stochastic optimization problem. The article presents several complementary approaches to solve a wide variety of single-objective and multiobjective mechanical engineering applications. Multiobjective optimization study and stochastic optimization studies are also discussed.

Finite element analysis is a computer-based numerical method for solving engineering problems in bodies of user-defined geometry. This article introduces the important issues of finite elements (especially accuracy and efficiency) in a nonacademic manner. It describes the Rayleigh-Ritz procedure for solving structural problems based on the principle of virtual work. The article discusses continuum elements, such as hexahedra, pentahedra, tetrahedra, quadrilaterals, and triangles, commonly used in three- or two-dimensional domains. It considers structural elements such as beam element, plate element, shell element, and elbow element. The article presents three examples to illustrate the types of problems that can be addressed and the decisions that must be made when using finite element analysis.

Powder metallurgy (PM) high-alloy tool steels (HATS) have unique properties that assist them in solving various problems related to machining of metal components. This article describes the cost-intensive PM processing routes of HATS, as well as their major properties, including elastic properties, density, mechanical properties, grindability, fatigue and wear resistance, and thermophysical properties.