{"product_id":"the-getme-mesh-smoothing-framework","title":"The GETMe Mesh Smoothing Framework","description":"High quality meshes play a key role in many applications based on digital modeling and simulation. The finite element method is a paragon for such an approach and it is well known that quality meshes can significantly improve computational efficiency and solution accuracy of this method. Therefore, a lot of effort has been put in methods for improving mesh quality. These range from simple geometric approaches, like Laplacian smoothing, with a high computational efficiency but possible low resulting mesh quality, to global optimization-based methods, resulting in an excellent mesh quality at the cost of an increased computational and implementational complexity.\n\nThe geometric element transformation method (GETMe) aims to fill the gap between these two approaches. It is based on geometric mesh element transformations, which iteratively transform polygonal and polyhedral elements into their regular counterparts or into elements with a prescribed shape. GETMe combines a Laplacian smoothing-like computational efficiency with a global optimization-like effectiveness. The method is straightforward to implement and its variants can also be used to improve tangled and anisotropic meshes.\n\nThis book describes the mathematical theory of geometric element transformations as foundation for mesh smoothing. It gives a thorough introduction to GETMe-based mesh smoothing and its algorithms providing a framework to focus on effectively improving key mesh quality aspects. It addresses the improvement of planar, surface, volumetric, mixed, isotropic, and anisotropic meshes and addresses aspects of combining mesh smoothing with topological mesh modification.\n\nThe advantages of GETMe-based mesh smoothing are demonstrated by the example of various numerical tests. These include smoothing of real world meshes from engineering applications as well as smoothing of synthetic meshes for demonstrating key aspects of GETMe-based mesh improvement. Results are compared with those of other smoothing methods in terms of runtime behavior, mesh quality, and resulting finite element solution efficiency and accuracy.\n\nFeatures:\n\n• Helps to improve finite element mesh quality by applying geometry-driven mesh smoothing approaches.\n\n• Supports the reader in understanding and implementing GETMe-based mesh smoothing.\n\n• Discusses aspects and properties of GETMe smoothing variants and thus provides guidance for choosing the appropriate mesh improvement algorithm.\n\n• Addresses smoothing of various mesh types: planar, surface, volumetric, isotropic, anisotropic, non-mixed, and mixed.\n\n• Provides and analyzes geometric element transformations for polygonal and polyhedral elements with regular and non-regular limits.\n\n• Includes a broad range of numerical examples and compares results with those of other smoothing methods.\u003cbr\u003eASIN: 1032094257\u003cbr\u003eVSKU: BVV.1032094257.G\u003cbr\u003eCondition: Good\u003cbr\u003eAuthor\/Artist:Vartziotis, Dimitris|Wipper, Joachim\u003cbr\u003eBinding: Paperback\u003cbr\u003e\u003cb\u003eNote:\u003c\/b\u003e Any images shown are stock photographs and product may differ from what is shown.  \u003cbr\u003e\u003cb\u003eCondition Notes\u003c\/b\u003e: The item shows wear from consistent use, but it remains in good condition and works perfectly. All pages and cover are intact  including the dust cover, if applicable . Spine may show signs of wear. Pages may include limited notes and highlighting. May NOT include discs, access code or other supplemental materials.  \u003cbr\u003e","brand":"Blue Vase Books","offers":[{"title":"Default Title","offer_id":43524230086717,"sku":"BVV.1032094257.G","price":61.44,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0589\/4225\/9261\/files\/1032094257-0.jpg?v=1787869313","url":"https:\/\/www.bluevasebooks.com\/products\/the-getme-mesh-smoothing-framework","provider":"Blue Vase Books","version":"1.0","type":"link"}