Using Higher Order Basis Functions - geomechanics/mpm GitHub Wiki
GIMP
TBA
Quadratic BSpline
To run a quadratic BSpline elements: ED2Q4P2B
(2D) and ED3H8P2B
(3D), additional settings should be added in the main .json
file.
"mesh": {
"cell_type": "ED3H8P2B",
"nonlocal_mesh_properties": {
"type": "BSPLINE",
"node_types": [
{
"nset_id": 0,
"dir": 0,
"type": 1
},
{...}
]
}
}
In the "nonlocal_mesh_properties"
section the following settings are required:
"type"
should be "BSPLINE"."node_types"
should be defined for each direction {0, 1, 2} for {x, y, z} following this convention:
//! Regular = 0 //Default
//! LowerBoundary = 1
//! LowerIntermediate = 2
//! UpperIntermediate = 3
//! UpperBoundary = 4
Reference:
- Steffen, M., Kirby, R. M., & Berzins, M. (2008). Analysis and reduction of quadrature errors in the material point method (MPM). International journal for numerical methods in engineering, 76(6), 922-948.
Local Maximum Entropy (LME)
To run the Local Maximum Entropy (LME) elements: ED2T3L
, ED2Q4L
(2D), and ED3H8L
(3D), additional settings should be added to the main .json
file.
"mesh": {
"cell_type": "ED2Q4L",
"nonlocal_mesh_properties": {
"type": "LME",
"gamma": XX,
"anisotropy": true, //optional default is false
"mesh_size": YY, //optional (if it is not given, an automatic computation will be done)
"support_tolerance": ZZ //optional default is 1e-6
}
}
In the "nonlocal_mesh_properties"
section the following settings are required:
"type"
should be "LME"."gamma"
is a non-dimensional thermalization parameter."anisotropy"
boolean to shift the metric tensor within the LME computation."mesh_size"
is the average mesh size, which is assumed to be constant in the current case."support_tolerance"
is the threshold magnitude of the shape function value.
Reference:
- Arroyo, M., & Ortiz, M. (2006). Local maximum‐entropy approximation schemes: a seamless bridge between finite elements and meshfree methods. International journal for numerical methods in engineering, 65(13), 2167-2202.