Image Denoising and Other Multidimensional Variational Problems

Temesgen Kindo September 21, 2018

We previously discussed how to solve 1D variational problems with the COMSOL Multiphysics® software and implement complex domain and boundary conditions using a unified constraint enforcement framework. Here, we extend the discussion to multiple dimensions, higher-order derivatives, and multiple unknowns with what we hope will be an enjoyable example: variational image denoising. We conclude this blog series on variational problems with some recommendations for further study.

Lire la Suite

Thomas Forrister September 20, 2018

After a pleasant day at the beach, you open your car door. It’s warm inside the vehicle, but it’s nothing a little air conditioning can’t fix. Then you sit down. The seat is burning hot, making for an uncomfortable ride home. Fortunately, there’s a way to avoid this scenario: Engineers can use thermoelectric devices that leverage the Seebeck and Peltier effects to control the temperature of car seats (among other applications).

Lire la Suite

Temesgen Kindo September 17, 2018

How do you find the shortest overland distance between two points across a lake? Such obstacles and bounds on solutions are often called inequality constraints. Requirements for nonnegativity of gaps between objects in contact mechanics, species concentrations in chemistry, and population in ecology are some examples of inequality constraints. Previously in this series, we discussed equality constraints on variational problems. Today, we will show you how to implement inequality constraints when using equation-based modeling in COMSOL Multiphysics®.

Lire la Suite

Thomas Forrister September 13, 2018

With the rise of 5G and other wireless millimeter-wave applications, there has been an increase in front-end antenna solutions that depend on monopole, dipole, and patch antennas. In these devices, the radiation efficiency tends to suffer due to the effect of lossy silicon substrate materials. Enter the dielectric resonator: Antennas using these resonators (made of nonmetallic materials) have a higher radiation efficiency. To increase directivity and gain at high frequencies, engineers can optimize dielectric resonator antenna (DRA) designs with simulation.

Lire la Suite

Catégories

Temesgen Kindo September 11, 2018

In the first part of this blog series, we discussed how to solve variational problems with simple boundary conditions. Next, we proceeded to more sophisticated constraints and used Lagrange multipliers to set up equivalent unconstrained problems. Today, we focus on the numerical aspects of constraint enforcement. The method of Lagrange multipliers is theoretically exact, yet its use in numerical solutions poses some challenges. We will go over these challenges and show two mitigation strategies: the penalty and augmented Lagrangian methods.

Lire la Suite

Bridget Paulus September 10, 2018

Schottky diodes are one of the oldest semiconductor components, but they are still found in many modern applications, including computers and radar systems. To ensure that a Schottky diode performs well, it’s important for engineers to accurately analyze factors like current density and barrier height in the design. As a benchmark model demonstrates, the COMSOL Multiphysics® software and add-on Semiconductor Module are well suited for this type of analysis.

Lire la Suite

Temesgen Kindo September 7, 2018

In the first part of this blog series, we discussed variational problems and demonstrated how to solve them using the COMSOL Multiphysics® software. In that case, we used simple built-in boundary conditions. Today, we will discuss more general boundary conditions and constraints. We will also show how to implement these boundary conditions and constraints in the COMSOL® software using the same variational problem from Part 1: (the soap film) — and just as much math.

Lire la Suite

Chandan Kumar September 5, 2018

To characterize hyperelastic materials, we need experimental data from a variety of tests, including subjection to uniaxial tension and compression, biaxial tension and compression, and torsion. Here, we show how to model the compression of a sphere made of an elastic foam using tension and compression test data obtained via uniaxial and equibiaxial tests. We demonstrate the use of the compressible Storakers hyperelastic material model for computation as well as how force-versus-stretch relationships are calculated for uniaxial and equibiaxial tests.

Lire la Suite

Temesgen Kindo September 4, 2018

What do soap films, catenary cables, and light beams have in common? They behave in ways that minimize certain quantities. Such problems are prevalent in science and engineering fields such as biology, economics, elasticity theory, material science, and image processing. You can simulate many such problems using the built-in physics interfaces in the COMSOL Multiphysics® software, but in this blog series, we will show you how to solve variational problems using the equation-based modeling features.

Lire la Suite

Thomas Forrister August 31, 2018

Hermann von Helmholtz was a German scientist, doctor, and philosopher who made advances in many scientific fields, including electrodynamics, optics, and thermodynamics. He invented several devices, such as the ophthalmoscope and the polyphonic siren, and is also known for the Helmholtz coil. By exploring the philosophy of science, Helmholtz made accurate connections about the laws of nature, perception, and empiricism.

Lire la Suite

Catégories

Brianne Costa August 30, 2018

In 1880, Alexander Graham Bell wrote a letter to his father, saying: “I have heard articulate speech by sunlight! I have heard a ray of the sun laugh and cough and sing!” He was talking about his latest success, the photophone, which he called his “greatest invention” shortly before his death. The photophone did not revolutionize the field of imaging, but an unintended effect Bell noticed while developing it did…

Lire la Suite

Catégories


Catégories


Tags

1 2 3 4 121