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Bioinformatics of the Brain

model. The basic concept behind the FEM is that a solution area may be

discretized—that is, replaced with an assembly of discrete elements—in order

to be mathematically modeled or approximated. These pieces may be utilized

to represent extremely complex forms because of the number of ways in which

they can be assembled. The concepts of finite element analysis go far further

back, even though the term “finite element method” was originally used in

1960 to tackle planar elasticity problems. The first usage of piecewise con-

tinuous functions defined over triangular domains in practical mathematics

literature dates back to 1943. The concept of minimizing a functional by lin-

ear approximation over sub-regions is established, in which values are supplied

at discrete places which fundamentally act as the node points of an element

mesh [6].

The problem becomes simpler by the finite element separation process,

that breaks a continuum into elements that can be a body of matter such as

a solid, liquid, gas, or just a patch of space. The unknown field variable is

then expressed in terms of presumptive approximation functions inside each

element [7]. The values that occur of the field’s variables at designated places

identified as nodes or nodal points are used to create the approximation func-

tions, which are additionally often referred to as interpolation functions. Nodes

often sit on the edges of elements when neighboring components are joined.

An element may have a few internal nodes in addition to its perimeter nodes.

The behavior of the field variable inside the elements is fully defined by the

nodal values of the field variable and the interpolation functions for the ele-

ments. Finite element method can be written with respect to dimensions as

shown in the following subsections [8].

6.3.1.1

One Dimensional Finite Elements

The one-dimensional ones are the initial and most basic kind. Throughout

its length, the area cross-section may change even while their area remains

constant. This is the issue with one-dimensional objects.

6.3.1.2

Two Dimensional Finite Elements

The two-dimensional area model uses two broad groups of components.

These forms are quadrilaterals and triangles. Higher order elements, including

quadratic and cubic, have either linear, curvilinear, or both types of edges.

Linear components in each family have linear edges. The first finite element to

be suggested for continuous problems was the triangle finite element. These

elements can be represented in xy plane [8].

6.3.1.3

Three Dimensional Finite Elements

The most commons are variations of two-dimensional elements such as tetra-

hedrons and parallelepipeds. One can examine it using a xyz coordinate plane.