Grid generation for the solution of partial differential equations

A general survey of grid generators is presented with a concern for understanding why grids are necessary, how they are applied, and how they are generated. After an examination of the need for meshes, the overall applications setting is established with a categorization of the various connectivity patterns. This is split between structured grids and unstructured meshes. Altogether, the categorization establishes the foundation upon which grid generation techniques are developed. The two primary categories are algebraic techniques and partial differential equation techniques. These are each split into basic parts, and accordingly are individually examined in some detail. In the process, the interrelations between the various parts are accented. From the established background in the primary techniques, consideration is shifted to the topic of interactive grid generation and then to adaptive meshes. The setting for adaptivity is established with a suitable means to monitor severe solution behavior. Adaptive grids are considered first and are followed by adaptive triangular meshes. Then the consideration shifts to the temporal coupling between grid generators and PDE-solvers. To conclude, a reflection upon the discussion, herein, is given

Design computing of complex-curved geometry using digital fabrication methods

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Architecture, 2006.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (leaves 64-65).The production of design information for digital fabrication is presented in this thesis. This thesis outlines the research of generating information for physical construction as architectural models of complex curved walls built from unique units. A series of computer programs and physical models as examples of orthogonal, non-orthogonal, and complex curved walls as designs were developed. The wall examples here are built of non-uniform, interlocking units using an integral connection approach. This is an exploration of design tools that construct complex curved structures in CAD for fabrication with a 3D printer. The thesis explores the evaluation processes used by architects when evaluating digitally fabricated desktop models. The research involved in this thesis takes the direction of investigating a new methodology for solving a modern and aesthetic approach to architecture. The research conducted investigates design as a way for synthesizing a grammatical (Stiny, 1977) approach as the systematic engine that is used to solve less systematic, curved, non-uniform form (Smithers, 1989).by Kenfield A. Griffith.S.M

Design operators

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Architecture, 2004.Includes bibliographical references (leaves 58-61).Design operators is a thesis that investigates the nature and characteristics of the design process by examining the interaction of computation with architectural design. The effects of the introduction of these media in design are traced and their quantitative and qualitative characteristics are identified. The thesis hints for an emerging design mentality delineated by the implementation, documentation and critical evaluation of a series of experimental projects in computational design.by Stylianos Dritsas.S.M

Computation with Curved Shapes: Towards Freeform Shape Generation in Design

Shape computations are a formal representation that specify particular aspects of the design process with reference to form. They are defined according to shape grammars, where manipulations of pictorial representations of designs are formalised by shapes and rules applied to those shapes. They have frequently been applied in architecture in order to formalise the stylistic properties of a given corpus of designs, and also to generate new designs within those styles. However, applications in more general design fields have been limited. This is largely due to the initial definitions of the shape grammar formalism which are restricted to rectilinear shapes composed of lines, planes or solids. In architecture such shapes are common but in many design fields, for example industrial design, shapes of a more freeform nature are prevalent. Accordingly, the research described in this thesis is concerned with extending the applicability of the shape grammar formalism such that it enables computation with freeform shapes. Shape computations utilise rules in order to manipulate subshapes of a design within formal algebras. These algebras are specified according to embedding properties and have previously been defined for rectilinear shapes. In this thesis the embedding properties of freeform shapes are explored and the algebras are extended in order to formalise computations with such shapes. Based on these algebras, shape operations are specified and algorithms are introduced that enable the application of rules to shapes composed of freeform B´ezier curves. Implementation of the algorithms enables the application of shape grammars to shapes of a more freeform nature than was previously possible. Within this thesis shape grammar implementations are introduced in order to explore both theoretical issues that arise when considering computation with freeform shapes and practical issues concerning the application of shape computation as a model for design and as a mode for generating freeform shapes

Fabricate

Bringing together pioneers in design and making within architecture, construction, engineering, manufacturing, materials technology and computation, Fabricate is a triennial international conference, now in its third year (ICD, University of Stuttgart, April 2017). Each year it produces a supporting publication, to date the only one of its kind specialising in Digital Fabrication. The 2017 edition features 32 illustrated articles on built projects and works in progress from academia and practice, including contributions from leading practices such as Foster + Partners, Zaha Hadid Architects, Arup, and Ron Arad, and from world-renowned institutions including ICD Stuttgart, Harvard, Yale, MIT, Princeton University, The Bartlett School of Architecture (UCL) and the Architectural Association