If your university does not require you to publish your dissertation as a book, I would be very reluctant to invest the time needed to get your dissertation published. I would put the PDF of your dissertation on your own website, making it available to everyone who wants to look at it. I would spend the time needed to rewrite your book on writing more peer reviewed articles. Either by publishing chapters from your dissertation, or by doing new research. I think publications are more important than a book, especially for someone like you who still has only a few publications.
In 1919, Marcel Tolkowsky published Diamond Design.He systematically analyzed the optics of a diamond. He estimated the best proportions for cuttinground brilliant diamonds. With minor changes, today's standardsfor "ideal cut" diamonds are based on Tolkowsky's book.
(I hope that this list of corrections would not turn out to be a long one.) If you discover any mistake (even a very small one) in the book or if you wish to be informed of any update in the (assuming that you possess a copy of the book), please let me know.
(2D Laplace equation, constant elements, Green's functions)
This chapter shows how the analyses and boundary element procedures in Chapters 1 and 3 for Laplace's and Helmholtz type equations can be extended to include three-dimensional problems.
I am posting here an for the book "A Beginner's Course in Boundary Element Methods" published by Universal Publishers.
The book explains the salient features (both theory and implementation details) of BEM in a very straight forward way, which helps a reader to quickly grasp the fundamentals and to start coding very soon.
I must say this is an excellent book and I have been able to get into an implementation of the problem I am trying to solve with BEM in a matter of hours.
A monograph is a very different body of work to a thesis. So, rather than sending out a proposal at once, and simply rewriting a chapter of the thesis to go with it, I ignored the advice and decided to think of the book as a new project. This involved taking key concepts from the thesis, but significantly reworking and developing them. This approach took a long time (three years, post-viva) because the work was undertaken alongside HPL teaching and summer work, which slowed the project down considerably.
However, the proposal I eventually submitted to Palgrave was a book proposal, rather than a modified thesis proposal. As such, the submission process was significantly easier; the project was accepted, a contract issued, and the completed manuscript took just three months to finish and submit. The book appeared in print just eight months later (less than a year after I first submitted the proposal.) I have no doubt that this was because I took that time to develop the project.
I published my PhD thesis as a book in VDM verlag. It publishes PhD dissertations and working with them is quite easy. The only problem is they put a relatively high price on your book and this might reduce the sale of your book. Due to this problem, I have received no royalty from my book yet. So if you think any other publisher can do better (financially) it is better you consider another publisher. Their publishing strategy is based on printing on demand. It means they publish a few copies of your book and sell them to some big libraries around the world. Then if an individual purchases your book online, they publish it for him as they receive the order.
I'm trying to couple BEM to the level set method for charged fluids and after reading a couple of books and getting thoroughly confused I found and followed your notes.