In general, finite difference methods are more successful if the accompanying grid has lines which are smooth and nearly orthogonal. This thesis discusses the development of an algorithm which produces such a grid when given the boundary description.
Topological considerations in structuring the grid generation mapping are discussed. In particular, this thesis examines the concept of the degree of a mapping and how it can be used to determine what requirements are necessary if a mapping is to produce a suitable grid.
The grid generation algorithm uses a mapping composed of bicubic B-splines. Boundary coefficients are chosen so that the splines produce Schoenberg's variation diminishing spline approximation to the boundary. Interior coefficients are initially chosen to give a variation diminishing approximation to the transfinite bilinear interpolant of the function mapping the boundary of the unit square onto the boundary of the grid.
The practicality of optimizing the grid by minimizing a functional involving the Jacobian of the grid generation mapping at each interior grid point and the dot product of vectors tangent to the grid lines is investigated.
Grids generated by using the algorithm are presented.
","abstract_html":"<p>In general, finite difference methods are more successful if the accompanying grid has lines which are smooth and nearly orthogonal. This thesis discusses the development of an algorithm which produces such a grid when given the boundary description.</p> <p>Topological considerations in structuring the grid generation mapping are discussed. In particular, this thesis examines the concept of the degree of a mapping and how it can be used to determine what requirements are necessary if a mapping is to produce a suitable grid.</p> <p>The grid generation algorithm uses a mapping composed of bicubic B-splines. Boundary coefficients are chosen so that the splines produce Schoenberg's variation diminishing spline approximation to the boundary. Interior coefficients are initially chosen to give a variation diminishing approximation to the transfinite bilinear interpolant of the function mapping the boundary of the unit square onto the boundary of the grid.</p> <p>The practicality of optimizing the grid by minimizing a functional involving the Jacobian of the grid generation mapping at each interior grid point and the dot product of vectors tangent to the grid lines is investigated.</p> <p>Grids generated by using the algorithm are presented.</p>","abstract_has_math":false,"creators":["Saunders, Bonita Valerie"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematics & Statistics","degree_department":null,"school":null,"contributors":["Philip W. Smith","John Tweed","Robert Smith","James Schwing"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1985,"date_issued":"1985-07-01T07:00:00Z","date_published":"1985-07-01T07:00:00Z","updated_at":"2026-07-24T03:35:23Z","subjects":["Grids","Computational fluids","B-splines","Mathematics"],"languages":[],"rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.odu.edu/mathstat_etds/103","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Philip W. Smith","John Tweed","Robert Smith","James Schwing"]},{"key":"dc:creator","label":"Author","values":["Saunders, Bonita Valerie"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2019-10-16T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics & Statistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Grids","Computational fluids","B-splines","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.odu.edu/mathstat_etds/103"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In general, finite difference methods are more successful if the accompanying grid has lines which are smooth and nearly orthogonal. This thesis discusses the development of an algorithm which produces such a grid when given the boundary description.
Topological considerations in structuring the grid generation mapping are discussed. In particular, this thesis examines the concept of the degree of a mapping and how it can be used to determine what requirements are necessary if a mapping is to produce a suitable grid.
The grid generation algorithm uses a mapping composed of bicubic B-splines. Boundary coefficients are chosen so that the splines produce Schoenberg's variation diminishing spline approximation to the boundary. Interior coefficients are initially chosen to give a variation diminishing approximation to the transfinite bilinear interpolant of the function mapping the boundary of the unit square onto the boundary of the grid.
The practicality of optimizing the grid by minimizing a functional involving the Jacobian of the grid generation mapping at each interior grid point and the dot product of vectors tangent to the grid lines is investigated.
Grids generated by using the algorithm are presented.
"]},{"key":"dc:title","label":"Title","values":["Algebraic Grid Generation Using Tensor Product B-Splines"]}]}],"canonical_facts":{"dc:contributor":["Philip W. Smith","John Tweed","Robert Smith","James Schwing"],"dc:creator":["Saunders, Bonita Valerie"],"dc:date.available":["2019-10-16T07:00:00Z"],"dc:description.abstract":["In general, finite difference methods are more successful if the accompanying grid has lines which are smooth and nearly orthogonal. This thesis discusses the development of an algorithm which produces such a grid when given the boundary description.
Topological considerations in structuring the grid generation mapping are discussed. In particular, this thesis examines the concept of the degree of a mapping and how it can be used to determine what requirements are necessary if a mapping is to produce a suitable grid.
The grid generation algorithm uses a mapping composed of bicubic B-splines. Boundary coefficients are chosen so that the splines produce Schoenberg's variation diminishing spline approximation to the boundary. Interior coefficients are initially chosen to give a variation diminishing approximation to the transfinite bilinear interpolant of the function mapping the boundary of the unit square onto the boundary of the grid.
The practicality of optimizing the grid by minimizing a functional involving the Jacobian of the grid generation mapping at each interior grid point and the dot product of vectors tangent to the grid lines is investigated.
Grids generated by using the algorithm are presented.
"],"dc:identifier":["https://digitalcommons.odu.edu/mathstat_etds/103"],"dc:rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
"],"dc:subject":["Grids","Computational fluids","B-splines","Mathematics"],"dc:title":["Algebraic Grid Generation Using Tensor Product B-Splines"],"thesis:degree_discipline":["Mathematics & Statistics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T03:35:23Z"}