3,099 research outputs found
Automatic grid construction for few-body quantum mechanical calculations
An algorithm for generating optimal nonuniform grids for solving the two-body
Schr\"odinger equation is developed and implemented. The shape of the grid is
optimized to accurately reproduce the low-energy part of the spectrum of the
Schr\"odinger operator. Grids constructed this way are applicable to more
complex few-body systems where the number of grid points is a critical
limitation to numerical accuracy. The utility of the grid generation for
improving few-body calculations is illustrated through an application to bound
states of He trimers
Optimizing the geometrical accuracy of curvilinear meshes
This paper presents a method to generate valid high order meshes with
optimized geometrical accuracy. The high order meshing procedure starts with a
linear mesh, that is subsequently curved without taking care of the validity of
the high order elements. An optimization procedure is then used to both
untangle invalid elements and optimize the geometrical accuracy of the mesh.
Standard measures of the distance between curves are considered to evaluate the
geometrical accuracy in planar two-dimensional meshes, but they prove
computationally too costly for optimization purposes. A fast estimate of the
geometrical accuracy, based on Taylor expansions of the curves, is introduced.
An unconstrained optimization procedure based on this estimate is shown to
yield significant improvements in the geometrical accuracy of high order
meshes, as measured by the standard Haudorff distance between the geometrical
model and the mesh. Several examples illustrate the beneficial impact of this
method on CFD solutions, with a particular role of the enhanced mesh boundary
smoothness.Comment: Submitted to JC
AN ENHANCED WAVELET BASED METHOD FOR NUMERICAL SOLUTION OF HIGH ORDER BOUNDARY VALUE PROBLEMS
The Legendre wavelet collocation method (LWCM) is suggested in this study for solving high-order boundary value problems numerically. Eighth, tenth, and twelfth-order examples are used as test problems to ensure that the technique is efficient and accurate. In comparison to other approaches, the numerical results obtained using LWCM demonstrate that the method's accuracy is very good. The results indicate that the method requires less computational effort to achieve better results
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Generalized partial differential equations for interactive design
This paper presents a method for interactive design by means of extending the PDE
based approach for surface generation. The governing partial differential equation is
generalized to arbitrary order allowing complex shapes to be designed as single patch
PDE surfaces. Using this technique a designer has the flexibility of creating and manipulating
the geometry of shape that satisfying an arbitrary set of boundary conditions.
Both the boundary conditions which are defined as curves in 3-space and the spine of the
corresponding PDE are utilized as interactive design tools for creating and manipulating
geometry intuitively. In order to facilitate interactive design in real time, a compact
analytic solution for the chosen arbitrary order PDE is formulated. This solution scheme
even in the case of general boundary conditions satisfies exactly the boundary conditions
where the resulting surface has an closed form representation allowing real time
shape manipulation. In order to enable users to appreciate the powerful shape design
and manipulation capability of the method, we present a set of practical examples
HIGH ORDER B-SPLINE COLLOCATION METHOD AND ITS APPLICATION FOR HEAT TRANSFER PROBLEMS
High order B-spline collocation for solving boundary value problem is presented in this paper. The approach employs high order B-spline basis functions with high approximation and continuity properties to handle problem domain with scattered or random distribution of knot points. Using appropriate B-spline basis function construction, the new approach introduces no difficulties in imposing both Dirichlet and Neumann boundary conditions in the problem domain. Several numerical examples in arbitrary domains, both regular and irregular shaped domains, are considered in the present study. In addition, simulation results concerning with heat transfer applications are further presented and discussed
Extension of the Finite Integration Technique including dynamic mesh refinement and its application to self-consistent beam dynamics simulations
An extension of the framework of the Finite Integration Technique (FIT)
including dynamic and adaptive mesh refinement is presented. After recalling
the standard formulation of the FIT, the proposed mesh adaptation procedure is
described. Besides the linear interpolation approach, a novel interpolation
technique based on specialized spline functions for approximating the discrete
electromagnetic field solution during mesh adaptation is introduced. The
standard FIT on a fixed mesh and the new adaptive approach are applied to a
simulation test case with known analytical solution. The numerical accuracy of
the two methods are shown to be comparable. The dynamic mesh approach is,
however, much more efficient. This is also demonstrated for the full scale
modeling of the complete RF gun at the Photo Injector Test Facility DESY
Zeuthen (PITZ) on a single computer. Results of a detailed design study
addressing the effects of individual components of the gun onto the beam
emittance using a fully self-consistent approach are presented.Comment: 33 pages, 14 figures, 4 table
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