1,577 research outputs found
On Basis Constructions in Finite Element Exterior Calculus
We give a systematic and self-contained account of the construction of
geometrically decomposed bases and degrees of freedom in finite element
exterior calculus. In particular, we elaborate upon a previously overlooked
basis for one of the families of finite element spaces, which is of interest
for implementations. Moreover, we give details for the construction of
isomorphisms and duality pairings between finite element spaces. These
structural results show, for example, how to transfer linear dependencies
between canonical spanning sets, or give a new derivation of the degrees of
freedom
Higher-order chain rules for tensor fields, generalized Bell polynomials, and estimates in Orlicz-Sobolev-Slobodeckij and bounded variation spaces
We describe higher-order chain rules for multivariate functions and tensor
fields. We estimate Sobolev-Slobodeckij norms, Musielak-Orlicz norms, and the
total variation seminorms of the higher derivatives of tensor fields after a
change of variables and determine sufficient regularity conditions for the
coordinate change. We also introduce a novel higher-order chain rule for
composition chains of multivariate functions that is described via nested set
partitions and generalized Bell polynomials; it is a natural extension of the
Fa\`a di Bruno formula. Our discussion uses the coordinate-free language of
tensor calculus and includes Fr\'echet-differentiable mappings between Banach
spaces.Comment: Submitte
Symmetry and Invariant Bases in Finite Element Exterior Calculus
We study symmetries of bases and spanning sets in finite element exterior
calculus using representation theory. The group of affine symmetries of a
simplex is isomorphic to a permutation group and represented on simplicial
finite element spaces by the pullback action. We want to know which
vector-valued finite element spaces have bases that are invariant under
permutation of vertex indices. We determine a natural notion of invariance and
sufficient conditions on the dimension and polynomial degree for the existence
of invariant bases. We conjecture that these conditions are necessary too. We
utilize Djokovic and Malzan's classification of monomial irreducible
representations of the symmetric group and use symmetries of the geometric
decomposition and canonical isomorphisms of the finite element spaces.
Invariant bases are constructed in dimensions two and three for different
spaces of finite element differential forms.Comment: 27 pages. Submitte
Smoothed projections over manifolds in finite element exterior calculus
We develop commuting finite element projections over smooth Riemannian
manifolds. This extension of finite element exterior calculus establishes the
stability and convergence of finite element methods for the Hodge-Laplace
equation on manifolds. The commuting projections use localized mollification
operators, building upon a classical construction by de Rham. These projections
are uniformly bounded on Lebesgue spaces of differential forms and map onto
intrinsic finite element spaces defined with respect to an intrinsic smooth
triangulation of the manifold. We analyze the Galerkin approximation error.
Since practical computations use extrinsic finite element methods over
approximate computational manifolds, we also analyze the geometric error
incurred.Comment: Submitted. 31 page
Corn (\u3ci\u3eZea mays L.\u3c/i\u3e) seeding rate optimization in Iowa, USA
Collecting soil, topography, and yield information has become more feasible and reliable with advancements in precision technologies. Combined with the accessibility of precision technologies and services to farmers, there has been increased interest and ability to make site-specific crop management decisions. The objective of this research was to develop procedures to optimize corn seeding rates and maximize yield using soil and topographic parameters. Experimental treatments included five seeding rates (61 750; 74 100; 86 450; 98 800; and 111 150 seeds ha-1) in a randomized complete block design in three central Iowa fields from 2012 to 2014 (nine site-years). Soil samples were analyzed for available phosphorus (Olsen method), exchangeable potassium (ammonium-acetate method), pH, soil organic matter (SOM), cation exchange capacity (CEC), and texture. Topographic data (in-field elevation, slope, aspect, and curvature) were determined from publically available light detection and ranging data. In four site-years, no interaction occurred between seeding rate and the descriptive variables. Three of the site-years resulted in a negative linear seeding rate response which made it impossible to determine an optimum seeding rate above the lowest seeding rate treatment. The seeding rate optimization process in five site-years resulted in seeding rate by variable interactions; four site-years had a single seeding rate by variable interaction (pH, in-field elevation, or curvature) and one site-year had three seeding rate by variable interactions (pH, CEC, and SOM). Meaningful seeding rate optimizations occurred in only three of nine site-years. There was not a consistent descriptive variable interaction with seeding rate as a result of weather variability. Referenc
Corn (Zea mays L.) seeding rate optimization in Iowa, USA
Collecting soil, topography, and yield information has become more feasible and reliable with advancements in precision technologies. Combined with the accessibility of precision technologies and services to farmers, there has been increased interest and ability to make site-specific crop management decisions. The objective of this research was to develop procedures to optimize corn seeding rates and maximize yield using soil and topographic parameters. Experimental treatments included five seeding rates (61 750; 74 100; 86 450; 98 800; and 111 150 seeds ha−1) in a randomized complete block design in three central Iowa fields from 2012 to 2014 (nine site-years). Soil samples were analyzed for available phosphorus (Olsen method), exchangeable potassium (ammonium-acetate method), pH, soil organic matter (SOM), cation exchange capacity (CEC), and texture. Topographic data (in-field elevation, slope, aspect, and curvature) were determined from publically available light detection and ranging data. In four site-years, no interaction occurred between seeding rate and the descriptive variables. Three of the site-years resulted in a negative linear seeding rate response which made it impossible to determine an optimum seeding rate above the lowest seeding rate treatment. The seeding rate optimization process in five site-years resulted in seeding rate by variable interactions; four site-years had a single seeding rate by variable interaction (pH, in-field elevation, or curvature) and one site-year had three seeding rate by variable interactions (pH, CEC, and SOM). Meaningful seeding rate optimizations occurred in only three of nine site-years. There was not a consistent descriptive variable interaction with seeding rate as a result of weather variability
Corn (\u3ci\u3eZea mays L.\u3c/i\u3e) seeding rate optimization in Iowa, USA
Collecting soil, topography, and yield information has become more feasible and reliable with advancements in precision technologies. Combined with the accessibility of precision technologies and services to farmers, there has been increased interest and ability to make site-specific crop management decisions. The objective of this research was to develop procedures to optimize corn seeding rates and maximize yield using soil and topographic parameters. Experimental treatments included five seeding rates (61 750; 74 100; 86 450; 98 800; and 111 150 seeds ha-1) in a randomized complete block design in three central Iowa fields from 2012 to 2014 (nine site-years). Soil samples were analyzed for available phosphorus (Olsen method), exchangeable potassium (ammonium-acetate method), pH, soil organic matter (SOM), cation exchange capacity (CEC), and texture. Topographic data (in-field elevation, slope, aspect, and curvature) were determined from publically available light detection and ranging data. In four site-years, no interaction occurred between seeding rate and the descriptive variables. Three of the site-years resulted in a negative linear seeding rate response which made it impossible to determine an optimum seeding rate above the lowest seeding rate treatment. The seeding rate optimization process in five site-years resulted in seeding rate by variable interactions; four site-years had a single seeding rate by variable interaction (pH, in-field elevation, or curvature) and one site-year had three seeding rate by variable interactions (pH, CEC, and SOM). Meaningful seeding rate optimizations occurred in only three of nine site-years. There was not a consistent descriptive variable interaction with seeding rate as a result of weather variability. Referenc
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