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Any numerical algorithm can be characterized in terms of its properties, which are accuracy, flexibility to handle many different problems, robustness, and computational efficiency in terms of amount of required coding and computational resources memory, storage and processor. Very often, it is difficult to achieve all of these properties in one particular algorithm. The aim of this book was that the reader, after hands on experience, can understand the fine details and strengths and weaknesses of each given solution’s methods sufficiently well and can adopt the suitable algorithm needed for their phase-field models. It is hoped that this objective was achieved by facilitating such comparative study with a collection of algorithms and case studies.