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172
Gerris: A TreeBased Adaptive Solver For The Incompressible Euler Equations In Complex Geometries
 J. Comp. Phys
, 2003
"... An adaptive mesh projection method for the timedependent incompressible Euler equations is presented. The domain is spatially discretised using quad/octrees and a multilevel Poisson solver is used to obtain the pressure. Complex solid boundaries are represented using a volumeoffluid approach. Sec ..."
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Cited by 97 (14 self)
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An adaptive mesh projection method for the timedependent incompressible Euler equations is presented. The domain is spatially discretised using quad/octrees and a multilevel Poisson solver is used to obtain the pressure. Complex solid boundaries are represented using a volumeoffluid approach. Secondorder convergence in space and time is demonstrated on regular, statically and dynamically refined grids. The quad/octree discretisation proves to be very flexible and allows accurate and efficient tracking of flow features. The source code of the method implementation is freely available.
Accurate Sum and Dot Product
 SIAM J. Sci. Comput
, 2005
"... Algorithms for summation and dot product of floating point numbers are presented which are fast in terms of measured computing time. We show that the computed results are as accurate as if computed in twice or Kfold working precision, K 3. For twice the working precision our algorithms for summa ..."
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Cited by 94 (15 self)
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Algorithms for summation and dot product of floating point numbers are presented which are fast in terms of measured computing time. We show that the computed results are as accurate as if computed in twice or Kfold working precision, K 3. For twice the working precision our algorithms for summation and dot product are some 40 % faster than the corresponding XBLAS routines while sharing similar error estimates. Our algorithms are widely applicable because they require only addition, subtraction and multiplication of floating point numbers in the same working precision as the given data. Higher precision is unnecessary, algorithms are straight loops without branch, and no access to mantissa or exponent is necessary.
Multiresolution Mesh Morphing
 PROCEEDINGS OF SIGGRAPH 99
, 1999
"... We present a new method for user controlled morphing of two homeomorphic triangle meshes of arbitrary topology. In particular we focus on the problem of establishing a correspondence map between source and target meshes. Our method employs the MAPS algorithm to parameterize both meshes over simple b ..."
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Cited by 83 (2 self)
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We present a new method for user controlled morphing of two homeomorphic triangle meshes of arbitrary topology. In particular we focus on the problem of establishing a correspondence map between source and target meshes. Our method employs the MAPS algorithm to parameterize both meshes over simple base domains and an additional harmonic map bringing the latter into correspondence. To control the mapping the user specifies any number of feature pairs, which control the parameterizations produced by the MAPS algorithm. Additional controls are provided through a direct manipulation interface allowing the user to tune the mapping between the base domains. We give several examples of sthetically pleasing morphs which can be created in this manner with little user input. Additionally we demonstrate examples of temporal and spatial control over the morph.
Design, Implementation and Testing of Extended and Mixed Precision BLAS
, 2001
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Mesh Generation
 Handbook of Computational Geometry. Elsevier Science
, 2000
"... this article, we emphasize practical issues; an earlier survey by Bern and Eppstein [24] emphasized theoretical results. Although there is inevitably some overlap between these two surveys, we intend them to be complementary. ..."
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Cited by 57 (8 self)
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this article, we emphasize practical issues; an earlier survey by Bern and Eppstein [24] emphasized theoretical results. Although there is inevitably some overlap between these two surveys, we intend them to be complementary.
Algorithms for QuadDouble Precision Floating Point Arithmetic
 Proceedings of the 15th Symposium on Computer Arithmetic
, 2001
"... A quaddouble number is an unevaluated sum of four IEEE double precision numbers, capable of representing at least 212 bits of significand. We present the algorithms for various arithmetic operations (including the four basic operations and various algebraic and transcendental operations) on quaddo ..."
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Cited by 55 (9 self)
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A quaddouble number is an unevaluated sum of four IEEE double precision numbers, capable of representing at least 212 bits of significand. We present the algorithms for various arithmetic operations (including the four basic operations and various algebraic and transcendental operations) on quaddouble numbers. The performance of the algorithms, implemented in C++, is also presented. 1.
A generic library of floatingpoint numbers and its application to exact computing
 In 14th International Conference on Theorem Proving in Higher Order Logics
, 2001
"... Abstract. In this paper we present a general library to reason about floatingpoint numbers within the Coq system. Most of the results of the library are proved for an arbitrary floatingpoint format and an arbitrary base. A special emphasis has been put on proving properties for exact computing, i. ..."
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Cited by 53 (6 self)
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Abstract. In this paper we present a general library to reason about floatingpoint numbers within the Coq system. Most of the results of the library are proved for an arbitrary floatingpoint format and an arbitrary base. A special emphasis has been put on proving properties for exact computing, i.e. computing without rounding errors. 1
Classroom examples of robustness problems in geometric computations
 In Proc. 12th European Symposium on Algorithms, volume 3221 of Lecture Notes Comput. Sci
, 2004
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Constrained Delaunay Tetrahedralizations and Provably Good Boundary Recovery
 In Eleventh International Meshing Roundtable
, 2002
"... In two dimensions, a constrained Delaunay triangulation (CDT) respects a set of segments that constrain the edges of the triangulation, while still maintaining most of the favorable properties of ordinary Delaunay triangulations (such as maximizing the minimum angle). CDTs solve the problem of enfor ..."
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Cited by 44 (1 self)
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In two dimensions, a constrained Delaunay triangulation (CDT) respects a set of segments that constrain the edges of the triangulation, while still maintaining most of the favorable properties of ordinary Delaunay triangulations (such as maximizing the minimum angle). CDTs solve the problem of enforcing boundary conformityensuring that triangulation edges cover the boundaries (both interior and exterior) of the domain being modeled. This paper discusses the threedimensional analogue, constrained Delaunay tetrahedralizations (also called CDTs), and their advantages in mesh generation. CDTs maintain most of the favorable properties of ordinary Delaunay tetrahedralizations, but they are more difficult to work with, because some sets of constraining segments and facets simply do not have CDTs. However, boundary conformity can always be enforced by judicious insertion of additional vertices, combined with CDTs. This approach has three advantages over other methods for boundary recovery: it usually requires fewer additional vertices to be inserted, it yields provably good bounds on edge lengths (i.e. edges are not made unnecessarily short), and it interacts well with provably good Delaunay refinement methods for tetrahedral mesh generation.
Approximate Boolean Operations on Freeform Solids
, 2001
"... In this paper we describe a method for computing approximate results of boolean operations (union, intersection, difference) applied to freeform solids bounded by multiresolution subdivision surfaces. ..."
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Cited by 41 (5 self)
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In this paper we describe a method for computing approximate results of boolean operations (union, intersection, difference) applied to freeform solids bounded by multiresolution subdivision surfaces.