Are there any similarities between the works of Dostoevsky and Ayn Rand's?

[Dostov]

are there?

[K.]

Perhaps on some level, but they are fundamentally opposed to each other in terms of philosophy and outlook.  Rand's glorification of the individual at the expense of all else is foreign to Dostoevsky (compare C&P with the Fountainhead).   The only thing I can imagine the two agreeing on would be a hatred of the communist regime that took over in Russia.

[Parsifal]

Rand was an admirer of Dostoyevsky, whom she read in the original Russian. 

She admitted that her 'sense of life' was the opposite of his, but always cited him as one of her great inspirations as a writer (second only to Victor Hugo). 

[SFG75]

I would argue that her characters have more in common with Zarathustra. 

[carnage_complex]

No.  Rand was well known for her 'larger than life' characters: Hank Rearden, Howard Roarke, Dagny Taggart, John Galt, etc.  Her writing is very melodramatic.  Dostoevsky's characters are way more emotively and psychologically ambiguous.  He was a major realist who also had a pronounced belief in the supernatural.  Rand had no interest in the afterlife or lack thereof.  Dostoevsky was a huge Slavophil.  Rand was not.  If the two of them have anything in common as people, it's their mutual hatred of communism.  Dostoevsky saw it as a means of bringing heaven to earth, the basic desire of a few twisted men.  Rand saw it as a pigsty run by a pack of incompetent 'moochers.'  Her views on Dostoevsky were very ambivalent.  She criticized him once on an interview for doting on his first wife, a woman who consensus claims that he never really loved after winning her away from the schoolmaster who was courting her after her first husband died.  Rand was only ever about Rand; she was an unabashed egoist, and were you to tell her this to her face, she would take this as a compliment.  Dostoevsky was all about something far different.  They both had a very strong faith, albeit of different kinds...and maybe it all boils down to the same thing, in the end.  But I doubt they would have gotten along.