Investigation of the effectiveness of interface constraints in the solution of hyperbolic second-order differential equations
Solutions to differential equations describing the behavior of physical quantities (e.g., displacement, temperature, electric field strength) often only have finite range of validity over a subdomain. Interest beyond the subdomain often arises. As a result, the problem of making the solution compati...
| Main Author: | |
|---|---|
| Format: | Others |
| Published: |
CSUSB ScholarWorks
2000
|
| Subjects: | |
| Online Access: | https://scholarworks.lib.csusb.edu/etd-project/1953 https://scholarworks.lib.csusb.edu/cgi/viewcontent.cgi?article=2953&context=etd-project |
| Summary: | Solutions to differential equations describing the behavior of physical quantities (e.g., displacement, temperature, electric field strength) often only have finite range of validity over a subdomain. Interest beyond the subdomain often arises. As a result, the problem of making the solution compatible across the connecting subdomain interfaces must be dealt with. Four different compatibility methods are examined here for hyperbolic (time varying) second-order differential equations. These methods are used to match two different solutions, one in each subdomain along the connecting interface. The entire domain that is examined here is a unit square in the Cartesian plane. The four compatibility methods examined are: point collocation; optimal least square fit; penalty function; Ritz-Galerkin weak form. Discretized L2 convergence is used to examine and compare the effectiveness of each method. |
|---|