Finite Element Method, shortly acronym for FEM is one of the major numerical techniques used in fields like physics, engineering, and other scientific areas for solving various complex problems. It is known to help in solving differential equations and more and is prized for its ability to handle difficult geometrics, non-linear material behavior, and other boundary conditions. As a result, FEM is widely used and is accepted as a significantly important means of computation.
The process of FEM involves using the numerical approach for approximating complex problems where various partial differential equations are subdivided from a complex domain into much smaller and simpler elements for calculations. This helps people like engineers, scientists, and more to depict the correct analysis and solve the problems. It has plenty of advantages and we’ll look to discuss more about it down below whilst also enlisting a few drawbacks of this method. Read along.
Advantages of Finite Element Method (FEM)
1. Versatile
FEM method is known for its versatile nature and the ability to apply to multiple problems across various areas of work. The range of problem-solving and equation-solving that the finite element method gives is unparalleled as it can help you in areas like simulating structural mechanics, fluid dynamics, heat transfer, electromagnetism, and more. FEM also helps in depicting the accurate solutions for these projects. Hence it has become a valuable tool for all scientists and engineers.
2. Accurate projections
Areas like structural engineering and fluid dynamics require accurate results. Even when the testing is being conducted, the approximations should match the real-world results. This is where FEM as a method is pretty useful as it can provide highly accurate solutions to these complex problems with ease. They also help in closely resembling the actual behavior of the system allowing the approximation of the correct levels. This accuracy is highly important for areas in engineering design and analysis part where even small errors can cause significant consequences.
3. Flexibility in Handling Geometry
The finite element method is known to handle various complex natures of geometrics and even boundary conditions with relatable ease. Since structural engineering and dynamics revolve around various irregular shapes and the intricate nature of structures, there’s always a hard time computing the values and representing them accurately. This is where FEM helps a lot as it allows for ease of access in terms of representing these systems and values to the closest levels and offers solutions for different boundary conditions and displacements. This is why FEM is known for being adaptable to a wide range of real-world conditions and scenarios.
4. Adaptive Mesh Refinement
Finite element methods allow adaptive mesh refinement where the mesh can be adjusted to help focus on the computational resources in the areas where they are much needed. This phenomenon comes in handy when working or handling problems that require exhibiting various levels of complex nature. FEM allows for computational resources and mechanisms to be efficiently distributed to the areas of need and hence reduces the computation and the overall storage requirements.
5. Option for Parallel Processing
FEM method allows for parallel processing where the computational task can be distributed across multiple processors or nodes and in turn reduce the time required for the computation of the solution. This ability and option to parallel processing has efficiently helped the harnessing of resources and apply large-scale simulations too without the need for varied computational equipment or methods.
Disadvantages of Finite Element Method (FEM)
1. Complex in Nature
FEM is very complex as it is a specialized numerical technique and hence requires a learning curve before being able to handle the workload or the process. It also requires a deep understanding of various principles of mathematics and engineering to be able to handle the tasks and perform the computations properly. This complexity in nature and the need for extensive understanding of the concepts can throw off beginners from entering the field.
2. High computational requirements
FEM is known to provide accurate solutions as per the need but the entire process requires significant computational prowess. This includes the need for processing power, memory modules, and high-performance computing clusters. All this means that there is a need for a significant resource which for normal organizations or smaller scale organizations can be hard to find.
3. Generation of Mesh
We aforementioned how FEM allows for adaptive mesh requirements but at the same time, those mesh and the generation of it require significant effort. Couple that with the common knowledge that the quality of the mesh will affect the accuracy of the results generated, the entire process can be complex and challenging. A poorly generated mesh can often lead to inaccurate results which will just add to the burden of going through the computation again from the start.
4. Can be difficult for Non-linearities
FEM is known to struggle with cases that involve strong non-linearities. Such cases where large deformations or material behaviors are exhibited require implicit and explicit formulations, which in itself won’t suffice at times. This just makes it a highly demanding and complex issue and can be hard to implement.
Final Words
The finite element method (FEM) is known to be a versatile and powerful numerical technique that helps in solving various problems related to engineering and scientific fields making it a valuable tool for scientists and engineers. It has multiple advantages as aforementioned that make it handy for use whilst also having a few drawbacks that we discussed. We hope this helps shed light on the concept of FEM.
