AXOM
Axom provides a robust, flexible software infrastructure for the development of multi-physics applications and computational tools.
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Defines the Lagrange family of Finite Elements. More...
#include </home/docs/checkouts/readthedocs.org/user_builds/axom/checkouts/v0.6.1/src/axom/mint/fem/shape_functions/Lagrange.hpp>
Static Public Member Functions | |
static CellType | getCellType () |
Returns the cell type of this instance. More... | |
static int | getType () |
Returns the Basis function type. More... | |
static int | getNumDofs () |
Returns the number of degrees of freedom on this Finite Element. More... | |
static int | getMaxNewtonIters () |
Returns the max number of newton iterations for this Finite Element. More... | |
static int | getDimension () |
Returns the dimension of the reference element. More... | |
static int | getMin () |
Returns the min coordinate of the element's reference space. More... | |
static int | getMax () |
Returns the max coordinate of the element's reference space. More... | |
static void | getCenter (double *AXOM_UNUSED_PARAM(center)) |
Returns the centroid of the reference element. More... | |
static void | getCoords (double *AXOM_UNUSED_PARAM(coords)) |
Returns the coordinates of the reference element. More... | |
static void | computeShape (const double *AXOM_UNUSED_PARAM(nc), double *AXOM_UNUSED_PARAM(phi)) |
Computes the shape functions of the Finite Element at the given natural coordinates, \( \xi \). More... | |
static void | computeDerivatives (const double *AXOM_UNUSED_PARAM(nc), double *AXOM_UNUSED_PARAM(phidot)) |
Computes the shape function first derivatives for the Finite Element at the given natural coordinates, \( \xi \). More... | |
Generic ShapeFunction API | |
static CellType | cellType () |
Returns the underlying cell type, e.g., MINT_QUAD, etc. More... | |
static int | type () |
Returns the Finite Element basis family type. More... | |
static int | numDofs () |
Returns the number of degrees of freedom. More... | |
static int | maxNewtonIters () |
Returns the maximum number of iterations for the Newton-Raphson. More... | |
static int | dimension () |
Returns the dimension of the reference element. More... | |
static double | min () |
Returns the min coordinate of the reference element. More... | |
static double | max () |
Returns the max coordinate of the reference element. More... | |
static void | center (double *center) |
Returns the center of the reference element. More... | |
static void | coords (double *coords) |
Returns the coordinates of the reference element. More... | |
static void | evaluate (const double *nc, double *phi) |
Evaluates the ShapeFunction at the given natural coordinates. More... | |
static void | derivatives (const double *nc, double *phidot) |
Evaluates the first derivatives of the shape function at the given natural coordinates. More... | |
Defines the Lagrange family of Finite Elements.
CELLTYPE | the cell type of the element, e.g., mint::QUAD, etc. |
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inlinestatic |
Returns the cell type of this instance.
References AXOM_STATIC_ASSERT, axom::mint::cellTypeToInt(), and axom::mint::NUM_CELL_TYPES.
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inlinestatic |
Returns the Basis function type.
References AXOM_STATIC_ASSERT, axom::mint::cellTypeToInt(), MINT_UNDEFINED_BASIS, and axom::mint::NUM_CELL_TYPES.
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inlinestatic |
Returns the number of degrees of freedom on this Finite Element.
References AXOM_STATIC_ASSERT, axom::mint::cellTypeToInt(), and axom::mint::NUM_CELL_TYPES.
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inlinestatic |
Returns the max number of newton iterations for this Finite Element.
References AXOM_STATIC_ASSERT, axom::mint::cellTypeToInt(), and axom::mint::NUM_CELL_TYPES.
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inlinestatic |
Returns the dimension of the reference element.
References AXOM_STATIC_ASSERT, axom::mint::cellTypeToInt(), and axom::mint::NUM_CELL_TYPES.
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inlinestatic |
Returns the min coordinate of the element's reference space.
References AXOM_STATIC_ASSERT, axom::mint::cellTypeToInt(), and axom::mint::NUM_CELL_TYPES.
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inlinestatic |
Returns the max coordinate of the element's reference space.
References AXOM_STATIC_ASSERT, axom::mint::cellTypeToInt(), and axom::mint::NUM_CELL_TYPES.
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inlinestatic |
Returns the centroid of the reference element.
[out] | center | ndims long buffer to store the centroid |
References AXOM_STATIC_ASSERT, axom::mint::cellTypeToInt(), and axom::mint::NUM_CELL_TYPES.
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inlinestatic |
Returns the coordinates of the reference element.
[out] | coords | ndims*ndofs long buffer to store the coordinates |
References AXOM_STATIC_ASSERT, axom::mint::cellTypeToInt(), and axom::mint::NUM_CELL_TYPES.
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inlinestatic |
Computes the shape functions of the Finite Element at the given natural coordinates, \( \xi \).
[in] | nc | natural coordinates at which to compute the shape functions |
[out] | phi | buffer (ndofs long) to store the shape functions |
References AXOM_STATIC_ASSERT, axom::mint::cellTypeToInt(), and axom::mint::NUM_CELL_TYPES.
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inlinestatic |
Computes the shape function first derivatives for the Finite Element at the given natural coordinates, \( \xi \).
[in] | nc | natural coordinates at which to compute the derivatives |
[out] | phidot | buffer (ndofs*ndims long) for the derivatives |
References AXOM_STATIC_ASSERT, axom::mint::cellTypeToInt(), axom::mint::getCellInfo(), axom::mint::NUM_CELL_TYPES, SLIC_ERROR, and axom::mint::UNDEFINED_CELL.
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inlinestaticinherited |
Returns the underlying cell type, e.g., MINT_QUAD, etc.
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inlinestaticinherited |
Returns the Finite Element basis family type.
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inlinestaticinherited |
Returns the number of degrees of freedom.
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inlinestaticinherited |
Returns the maximum number of iterations for the Newton-Raphson.
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inlinestaticinherited |
Returns the dimension of the reference element.
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inlinestaticinherited |
Returns the min coordinate of the reference element.
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inlinestaticinherited |
Returns the max coordinate of the reference element.
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inlinestaticinherited |
Returns the center of the reference element.
[out] | center | buffer (ndims long) to store the centroid |
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inlinestaticinherited |
Returns the coordinates of the reference element.
[out] | coords | buffer (ndims*ndofs long) to store the coordinates |
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inlinestaticinherited |
Evaluates the ShapeFunction at the given natural coordinates.
[in] | nc | natural coordinates at which to compute the shape functions |
[out] | phi | buffer (ndofs long) to store the shape function. |
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inlinestaticinherited |
Evaluates the first derivatives of the shape function at the given natural coordinates.
[in] | nc | natural coordinates at which to compute the derivatives |
[out] | phidot | buffer (ndofs*ndims long) to store the derivatives |