6,791 research outputs found
The Virtual Element Method with curved edges
In this paper we initiate the investigation of Virtual Elements with curved
faces. We consider the case of a fixed curved boundary in two dimensions, as it
happens in the approximation of problems posed on a curved domain or with a
curved interface. While an approximation of the domain with polygons leads, for
degree of accuracy , to a sub-optimal rate of convergence, we show
(both theoretically and numerically) that the proposed curved VEM lead to an
optimal rate of convergence
Basic principles of hp Virtual Elements on quasiuniform meshes
In the present paper we initiate the study of Virtual Elements. We focus
on the case with uniform polynomial degree across the mesh and derive
theoretical convergence estimates that are explicit both in the mesh size
and in the polynomial degree in the case of finite Sobolev regularity.
Exponential convergence is proved in the case of analytic solutions. The
theoretical convergence results are validated in numerical experiments.
Finally, an initial study on the possible choice of local basis functions is
included
Serendipity Face and Edge VEM Spaces
We extend the basic idea of Serendipity Virtual Elements from the previous
case (by the same authors) of nodal (-conforming) elements, to a more
general framework. Then we apply the general strategy to the case of
and conforming Virtual Element Methods, in two and three dimensions
Serendipity Nodal VEM spaces
We introduce a new variant of Nodal Virtual Element spaces that mimics the
"Serendipity Finite Element Methods" (whose most popular example is the 8-node
quadrilateral) and allows to reduce (often in a significant way) the number of
internal degrees of freedom. When applied to the faces of a three-dimensional
decomposition, this allows a reduction in the number of face degrees of
freedom: an improvement that cannot be achieved by a simple static
condensation. On triangular and tetrahedral decompositions the new elements
(contrary to the original VEMs) reduce exactly to the classical Lagrange FEM.
On quadrilaterals and hexahedra the new elements are quite similar (and have
the same amount of degrees of freedom) to the Serendipity Finite Elements, but
are much more robust with respect to element distortions. On more general
polytopes the Serendipity VEMs are the natural (and simple) generalization of
the simplicial case
Lowest order Virtual Element approximation of magnetostatic problems
We give here a simplified presentation of the lowest order Serendipity
Virtual Element method, and show its use for the numerical solution of linear
magneto-static problems in three dimensions. The method can be applied to very
general decompositions of the computational domain (as is natural for Virtual
Element Methods) and uses as unknowns the (constant) tangential component of
the magnetic field on each edge, and the vertex values of the
Lagrange multiplier (used to enforce the solenoidality of the magnetic
induction ). In this respect the method can be seen
as the natural generalization of the lowest order Edge Finite Element Method
(the so-called "first kind N\'ed\'elec" elements) to polyhedra of almost
arbitrary shape, and as we show on some numerical examples it exhibits very
good accuracy (for being a lowest order element) and excellent robustness with
respect to distortions
Recognizing Activities of Daily Living of People with Parkinson's
Tese de mestrado, Informática, Universidade de Lisboa, Faculdade de Ciências, 2022Parkinson's disease is a common neurodegenerative disease that affects a large
part of the world's population. This disease involves a lot of symptoms, however the
most prevalent is the change in the patient's movements or even the loss of
functionality. There is no treatment, however it exists medication that relieves and
reduces the symptoms for a period. A Parkinson’s patient needs to be watched by
clinicians to understand if the medication is working correctly and to analyse the disease
progression. The current way of doing this evaluation is at clinics where the patient
needs to go to the clinic or to live there. With this into consideration it was requested a
monitoring system of activities of daily living for Parkinson’s patient.
The monitoring system consists in a mobile application in an Android smartphone
serving as a diary for the patient of clinician to record the activities done at that
moment. With this application, the patient needs to wear an accelerometer in the wrist to
gather the acceleration in the 3-axis. The application besides the monitoring function, it
gives the ability to the clinician to schedule lists of activities for the patient to do during
the day, allowing the clinician to have some control.
We carried out a study with 10 healthy participants which used the monitorization
system for 3 days each. The patient would worn the accelerometer and record the
activities that they would do throughout the day, was asked a minimum of 5 activities
per day. Alongside this recording it was schedule 1 list of activities to be carried out
each day, this list only had motor activities such as walk, sit down, and stand up. At the
end of each participant study, it was made a questionnaire with standard usability
questions and an interview that helped us understand if the system was reliable or not
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